It is true that in addition to bolting on correct features, you occasionally need syntheses that simplify the whole thing, like how the zoo of mesons and baryons were explained by quarks. But at the moment, we're very far from having that problem...

Consider the Many-Worlds Interpretation[0] of quantum mechanics. Its proponents say you need just a pretty small assumption (the Universe branches under certain conditions), and its critics say assumption is a huge deal, because it postulates an astronomically high (erm, cosmologically high) number of Universes that we can't observe.

[0]: https://en.wikipedia.org/wiki/Many-worlds_interpretation

> Would it be reasonable to think of the "true model" of the universe as having infinite complexity, and we are trying to approximate it by adding features and interactions stepwise?

Nobody knows.

So far, we have very successful theories (general relativity, quantum field theory) that rely on a small number of equations with a small number of terms each. That gives hope that at least the laws that govern the Universe are not infinitely complex, but we cannot really know for sure.

Short version's probably that we don't quite have enough data to compellingly argue for excessively elaborate descriptions.

I mean, yeah, every time there's any little observation -- even one that's not anywhere near statistically significant -- there's technically a tiny bit of information in it that could, in principle, be used to better inform a model than a model that excludes it. But at current, folks don't tend to care; too much mental/computational overhead for too little payoff.

Cows in Physicsland aren't spherical because physicists couldn't conceive of more precise descriptions, but rather because non-spherical cows were too much work.