> But the real question is whether it is a _useful_ modeling language for everything.
Category theory is definitely not useful for modeling everything. However, it's useful for modeling a whole lot. Categories have few axoims, and those they do have align well with how humans break down complex problems, so a lot of systems can be modeled neatly with categories. And category models are useful for proving existence, uniqueness, and notions of "maximum" and "minimum" for their "arrows", which are often useful things people try to prove about systems.
Category theory is definitely not useful for modeling everything. However, it's useful for modeling a whole lot. Categories have few axoims, and those they do have align well with how humans break down complex problems, so a lot of systems can be modeled neatly with categories. And category models are useful for proving existence, uniqueness, and notions of "maximum" and "minimum" for their "arrows", which are often useful things people try to prove about systems.