There is a simple, straightforward reason that memetics has not 'caught on' and become more widely accepted: the concept underlying it — depending on how one interprets the term 'meme' — are either philosophically derivative or nonsensical pseudoscience. The mere fact that I have to qualify that statement by pointing out that the term 'meme' is in dire need of an empirical or rational definition should point to the troubles here. If the core concept is that intellectually squishy, what can we do with it?
If we take the term 'meme' to be an abstract pointer to certain kinds of basic understanding that can be transmitted from person to person, then this topic has been deeply covered by anthropology, sociology, psychology, European social theory, and modern language theory. The entire concept of 'culture' (which has its roots in the 19th century) is based on the idea that worldviews are passed down across generations, changing and resisting change across time. Memetics would only seem novel to someone who has limited their reading to the Anglophone analytic philosophy tradition, carefully excluding the later Wittgenstein and some of APs more critical voices. Granted that I understand why this is. Empiricist philosophy has tried gamely to eliminate subjectivity from its worldview, and thus has avoided any proper study of the human mind; Dawkins is introducing 'mentalist' concepts by framing them in a 'physicalist' analogy to evolution, but Dawkins is not presenting a new concept by any means.
On the other hand if we take the term 'meme' to refer to some actual object — be it cognitive, mental, neurobiological, or whatnot — then Dawkins has left anything resembling science behind and stepped into the realm of speculative fiction. What and where are these 'meme' objects? Can we point at one? Can we slice it out and put it under a microscope? I can reasonably say "I ate six incredible memes before breakfast" and there is not a single thing you can do to tell me I didn't. That's pseudoscience to the core.
I know that the term 'meme' has taken on a life of its own in the popular literature. It's now something like what used to be called an 'ear-worm' (a little bit of music you can't get out of your head), except done in visual media. That's perfectly adequate as popular slang, but is neither a scientific nor philosophical proposition. The main theory hasn't caught on because it's not really saying anything new that isn't better discussed elsewhere (except, as I noted, for Anglophone analytic philosophers, who still don't really want to embrace mentalism in any form and push back against ideas of this sort). Maybe if it develops further it will catch on, but as a theory it is currently too weak to survive the 'evolutionary' competition it presupposes.