Except non-local deterministic theories are much more complicated and almost impossible to use. That's why a lot of physicists regard the result as showing that reality is both non-local and non-deterministic. Very few suspect a non-local hidden variables theory.

I think that non-determinism would be an extraneous assumption given the fundamental randomness apparent in quantum measurements. In my opinion, hidden variables are something extra to add to take account of this, and indeed it's very difficult to use Bohmian mechanics with relativity etc.