Because this opinion has surfaced a number of times here: Yes, Tolkien did care deeply about the realism of his world. And because he spent his whole life studying pre-modern societies, the societies he creates in Middle Earth do function very realistically. I think there are two reason why many readers miss this:

(1) Much of Tolkien's world-building is implicit rather than explicit. He doesn't talk about Aragorn's tax policy because he doesn't need to; Aragorn is recognisably a feudal king and there is a standard way taxes are done a feudal system (i.e. the vassals take care of gathering them). Tolkien has a deep understanding of how such societies function, but much of this comes out indirectly in the story, through the way the characters behave and what they can and cannot do.

(2) Pre-modern societies are so deeply different from modern ones (economically, culturally, and socially) that I think many readers stumble across things they find unexpected and dismiss it as "unrealistic fantasy", without understanding that in such a context, this is exactly how one would expect the world to work. For example, the deep devotion and self-sacrificial service Sam shows to Frodo is often discussed in terms of friendship (and it is a great friendship), but one cannot fully understand it unless one also understands it as a (very positive) master-servant relationship.

If you want a better understanding of the deeper realism of LotR, I cannot recommend Bret Devereaux' blog highly enough. He is an ancient military historian and has written extensive (but entertaining!) analyses of both LotR and GoT. See here for two samples: https://acoup.blog/2020/05/22/collections-the-battle-of-helm..., https://acoup.blog/2019/05/28/new-acquisitions-not-how-it-wa...