> I suspect some future generation is going to decide that diagonalizaation is based on questionable axioms. It leads to invisible pink elephants.

Past generations of course were not always comfortable with it either, but.. No one shall expel us from the paradise that Cantor has created for us.

https://en.m.wikipedia.org/wiki/Cantor%27s_paradise

It’s useful I think to have a conservative impulse somewhere as a counterpoint to wild invention, and math has benefited a lot from the constructivist vs formalist debate.