The same analysis will apply to many forms of academic endeavor, such as theoretical science, philosophy, arts, ancient history, and some others I have neglected due to my faulty memory.
There are many types of motivation for studying such topics. And many different motivations for support from the wider community. No single motivation is going to explain the entire activity.
Aesthetics will certainly motivate some people. There are also related and overlapping enjoyment features. Some people love puzzles, for example. Some people love to seek knowledge, especially new knowledge. Some people love to create their art. Generically, such enjoyment arises because humans have "big brains" and it is, for many, enjoyable using them. Different abstract studies will have different components of these related attractions.
And the enjoyment will result in many people wanting to give support to such study, even if they cannot do it professionally. This is the reason the Perimeter Institute exists. A guy became an engineer, invented a type of cell phone, and made a ton of money. But his first academic love was always theoretical physics. So he endowed them with a bunch of money. Then he got his business partners to add to the endowment. Then he persuaded the province to add more. And now, the place is pretty secure.
Practical application is a motivating factor even for the most seeming abstract academic of studies. As an example that is comforting to me (due to my background in theoretical physics) consider Grassmann numbers. This is a very unusual algebra of numbers that have the peculiar property that their square is zero. It turns out these are useful in understanding the behavior of elctrons. And in turn, that is useful in understanding certain physics experiments. Which in turn are useful in understanding certain types of electronics. Which in turn helped advance the study of semiconductors. Which you are presumably looking at to read this on some type of computer.
Or, to take a quote form Isaac Asimov:
There is a single light of science, and to brighten it anywhere is to brighten it everywhere.
Another motivation is as a way to detect and nurture ability. One place wants cryptographers. Another wants computer programmers. Another wants people with the ability to understand enormous databases of seemingly unrelated data. Another wants to detect and predict trends. Another wants to understand the behavior of groups under various stress conditions. The ability to do abstract maths is useful to predict ability at these other tasks. The mental processes to do maths will train one to understand and solve a wide variety of problems. And those problems have application in a wide variety of applications.
Such motivations also have some ability to get support for study other than math. History, for example, can often help a military officer understand an opponent. Art theory can contribute to understanding marketing. Linguists can contribute to making computer interfaces easier to use. And so on over nearly any academic study.
There are, of course, less rarified motivations. Abstract academic studies have prestige and garner respect. Various granting agencies and political groups are often motivated by this prestige. So a politician may find it useful to advocate for grants to be given to a university including the departments doing such abstract studies. Such support does not necessarily flow in any strong relationship to anybody's evaluation of the worth of such studies. It flows in relation to a politician's perception of the prestige it produces for him.