Introduction: Is the thesis correct?
There are some authors who surely thought that way. Just to give a few:
It is impossible to exaggerate the importance of grasping the supreme
principle of morality; and because Kant's Groundwork of the Metaphysics
of Morals (as I call his Grundlegung zur Metaphysik der Sitten) treats of this,
topic, and of this topic alone, it is an indispensable book for all who
profess to think seriously about moral problems. (Paton, The Categorical Imperative: A study in Kant's Moral Philosophy, 1947, p.15)
Paton states that it is "indispensable" for "serious" ethical thinking and delivers a first argument for why it is so good for learning about ethics: It is about the supreme principle and that alone.
Thus, I believe that the Kantian view might be better described as the priority of (the moral) law over the good. And it is the fact that the GMS is the first work in which Kant expressed this priority, which is inseparably connected with his conceptions of autonomy and the categorical imperative, that makes it the single most important contribution to modern moral philosophy. (Allison, Kant's Groundwork for the Metaphysics of Morals: A Commentary, 2011, pp. 2-3)
Allison puts it in a more historical perspective, stating that the "discovery" of autonomy and the systematic usage of heteronomy are a milestone and nothing short of his "Copernic revolution" in theoretical philosophy (see pp. 1-2). He also adds:
Like any great philosophical work, GMS is inexhaustible. Thus, I am confident that, if two hundred years from now people are still studying and reflecting upon philosophical texts, GMS will continue to be prominent amongst them. (Allison 2011, p.3)
Adding Allen W. Wood into this illustrious circle (see quotes by him later on) that makes three of the most prolific Kant scholars in history agreeing in that it is his most important piece of writing on ethics for various reasons.
This answer will provide three different general reasons (the first one kind of including/following from the other two) for its popularity in addition to the above quotes and after that, a short remark on why this may be understandable, but in fact is quite problematic.
1. It is part of almost every curriculum in academic philosophy
One factor definitely is that it is the book of Kant that is lectured on the most in universities. But why is that the case (other than what Paton and Allison wrote and I already mentioned)?
It has a length allowing for being read and discussed quite thoroughly in one term and at the same time has quite an elaborate, stringent argument going through all of the text. It is both systematic (something the essays and Metaphysics of Morals lack) and with examples (other than the completely theoretical Critique of Practical Reason). All of them are good reasons to read the Groundwork.
Allen Wood offers another very good reason why it's read in academia in the introduction to his Yale translation (2002):
Kant’s little book of 1785 is one of the most signiﬁcant texts in the history of
ethics. It has been a standard of reference — sometimes a model to be developed and expanded on, sometimes a target of criticism — for moral philosophers from the German idealist and German Romantic traditions, for Victorians of the utilitarian school such as Mill and Sidgwick, for later British
idealists such as Green and Bradley, for the neo-Kantians, for twentieth-century philosophers in both the continental and the anglophone traditions,
and for moral philosophers of all persuasions right down to the present day.
From the standpoint of the depth and originality of the ideas it contains, it
undoubtedly deserves this inﬂuence. (page ix)
In short: It both offers the possibility for getting an idea of the core of Kant's own ethical thought (containing all important concepts and terminology) and has been the standard reference for authors throughout the history of philosophy when dealing with deontological (duty-based) ethics. Without understanding the idea, you miss on one quite influential line of ethical thought completely.
2. Weaknesses of other ethical writings of his
The weaknesses I point out here can mostly be turned around to be taken in favour of the Groundwork.
Critique of Pure Reason
Contains ethical parts in the Canon of Pure Reason, the last chapter. Those parts are quite sketchy, already containing many concepts and conceptual links that are better established later. In addition, it contains a very problematic circular reasoning (see Förster, The Twenty-Five Years of Philosophy, 2012, p. 48-53).
Addition as (rightfully) requested by @virmaior: The ethical theme (as hinted at by the title of the chapter) is just embedded into and set in relation to the theory of knowledge that is set out over the course of the rest of the book. It is, therefore, futile to try to extract the ethical parts and read them in isolation for everyone but people who are already Kant specialists.
All these points make the book a bad choice for reading about Kant's ethical thought.
Critique of Practical Reason
His most elaborate systematic work on ethics, this has two main problems:
First, due to reasons of argumentation, the categorical imperative is simply stated to be a "fact of reason" (Ak. 5:8). Without having read the Groundwork, this idea is completely unintelligible (he refers to the derivation of the content of the CI in the Groundwork as still correct in a footnote).
Also, this book is very technical and quite long compared to the Groundwork. Too much for a seminar to chew in one term completely and at the same time almost impossible to understand without a thorough discussion with a knowledgeable person (applies to the first critique just as well, if not even more). It's not something you are able to read on your own simply out of interest.
Another problematic factor is his recourse to the soul and God as necessary ideas for making his ethics work. Something quite problematic in our secular times.
While the essays are indeed masterpieces and a much better read than most other pieces by Kant, they pay with systematicity. Those essays elaborate concepts and thoughts you can hardly completely understand without having read their systematic foundations, one of which the Groundwork provided (within limits, see at the end of this answer). Because of this, they sometimes can seem quite otherworldly for people not sharing the mindset anyway.
The Metaphysics of Morals
Without question an important book, quite long, too. Main problem here is the very assertive style. There are many points just stated without further argument, oftentimes arguments given are counter-arguments against arguments brought forward against earlier writings. Taken as a stand-alone that makes it quite useless other than to inform on Kant's opinions on various issues. Given he's a child of his time, those can seem quite strange from time to time.
Often forgotten, though even more important than the MM, IMHO. Shares many problems of the Metaphysics as written and contains many aspects that are clarifying and taking further, but not much regarding the core and foundation of his ethical thought.
Also, this text introduces new and breaks with some previous thoughts, sometimes in a rather subtle way, other times quite radically. Without knowledge of his previous works the complexity of the Religion is way too much to handle (thanks again @virmaior for the point)
3. The analytical method
Let us [...] turn directly to the Groundwork and hence to “the search for and establishment of the supreme principle of morality.” Here the most suitable approach is the analytical method
that Kant himself had just employed with success in the Prolegomena and
which in addition to clarity in the steps of the argument also holds out the
promise of popularity (Förster, 2012, p. 58, emphasis mine).
One should not underestimate this factor. Kant explicitly starts with our everyday moral intuitions (one should do a moral deed because it is the right thing to do, not because it happens to be good for something [i.e. myself or something I want/like]). He basically just spells out what is actually linguistically and logically implied in this kind of thought. In that, he is indeed quite close to modern "analytic philosophy" if one is able to bear in mind the language and common mindset of the time. Also, this puts aside or at least weakens many religious connotations that seem out-of-date for many people these days.
4. Problems with singling out the Groundwork
Wood writes in his preface:
[I]n the development of Kant’s own
moral thinking, it [i.e. the Groundwork] occupies a place that ought to make us question the
wisdom of treating it, the way moral philosophers customarily do, as the
deﬁnitive statement of Kant’s views on ethics. (ix)
He clarifies this point later and I wholeheartedly agree with him, adding the Anthropology to the list:
Kant’s essays and treatises of the 1790s, and especially the Metaphysics
of Morals (1798), give us explicit accounts of many matters on which
readers of the Groundwork customarily try to deduce the ‘‘Kantian view’’
(by triangulation, as it were) from what he says in this little foundational
treatise. Many doctrines standardly attributed to Kant on the basis of these
triangulations — on topics such as the nature of moral motivation, the relation between reason and feeling in human action, the structure of everyday
moral reasoning, and the nature of the will’s freedom — do not harmonize
very well with what Kant actually says in the Metaphysics of Morals,
Religion within the Boundaries of Mere Reason, or other later works.
That means despite its various advantages as an introduction to Kant's ethical thought, the Groundwork is revised and clarified in a lot of points in the later writings. In the end, you get a first grasp of the very core of his ethics, but everything else is depending on mere guesswork (what Wood calls "triangulation"). Beside confirming that it is the common theme that academics inform themselves regarding Kantian ethics often by reading the Groundwork only, Wood points out that the picture they get is incomplete at best and the things they develop from there are distortions of what Kant actually thought when you consider all of his ethical texts. Allison gives Ross (1954) as an example of that very problem (Allison 2011, p.3, fn.11).
No wonder so many people accused Kant of being completely inapplicable and lacking any accounts of how the CI could possibly motivate anyone. They just took the Groundwork (or, as Allison states in the footnote just mentioned, the second Critique plus Groundwork) to be representing all of Kant's thinking regarding ethics. Considering Kant's later distinction between "schooling" philosophy and "philosophy of the world" which is "pragmatic" and about being a "citizen of the world" (better translation could be "cosmopolitan")
(Anthropology, 7:120), it becomes clear that this narrow understanding can only represent the "schooling" part, but what's ethics as long as it does not become "pragmatic" or, more simple, practical?