As far as I understand it, the situation is this:-

The Schwarzschild solution to Einstein's equations is the simplest possible form and simply proves that black holes can exist. It neglects angular momentum & charge for the sake of simplicity.

The Kerr solution incorporates angular momentum, and is a more comprehensive solution for this. Going beyond the Kerr solution is the Kerr-Newman solution which incorporates angular momentum & charge.

Rotation is believed to be the norm for any compact object, and that includes black holes.