[CuriouslyC]

If we want to put physics on the faith table, I'm cool with whatever anyone wants to believe, and more power to them. But you can't be objectively right on the faith table - that's the price of admission.

If we want to be "true" and fully rational then we need to try to accurately represent our degree of knowledge about the world. Thus we shouldn't be making strong statements about things with an absence of evidence.

[sirclueless]

I wouldn't say assuming infinite density of black holes involves an absence of evidence. It is a hypothesis made in advance of evidence, and it leads to specific predictions that should be falsifiable, and in that sense it's considered scientifically sound.

As for implications that can't be falsified, for example ones that (to butcher Douglas Adams) "rather involve being on the other side of the event horizon," scientists can and do feel free to disregard those. Contradictory assumptions by scientists do not imply that one of them is "wrong" unless their theories imply contradictory observable phenomena. In which case there is probably a fruitful experiment to be done.