marduk
quelling chaos since 2352BC
That's the problem with theoretical physics. At a certain point, it stops being physics (a science which describes reality), and starts being philosophical speculation with no basis in reality.
At that point the philosopher can even abandon mathematical coherence and do irrational things like divide by zero.
The end result is millions of kids sitting around watching ridiculous television shows about nonsense like black holes and and star mass objects supposedly spinning at millions of RPM or 24% the speed of light.
Math is not the real universe. It's a model of how we think the universe exists. So I agree that theoretical physics does not always predict the universe. Just look at the profound failure of string theory.
At any rate, just because the theory predicts it, doesn't mean that black holes reach actual infinite density. There may be an unknown inflationary pressure which keeps it really dense (therefore acting a lot like a black hole) but not infinitely dense.
Nobody knows for sure.