There seems to be a consensus that quantum theory has to be intrinsically random, as well as various claims that you can’t have a classical model of quantum theory and that you can have a local model of quantum theory, as long as you’re willing to sacrifice realism.

I think that much of this is poorly thought out. I’ve written about this at http://quantropy.org/19/, but essentially, it is always possible to replace intrinsic randomness in a model by pseudo-randomness (possibly some sort of chaotic system), without affecting the model greatly. And what does realism mean? If it means determinism as opposed to randomness, well randomness certainly doesn’t help you to keep locality. In the end realism doesn’t seem to mean anything very much.

As for the claim that quantum theory can’t have a classical model, this seems incoherent to me. You can do calculations in quantum theory, and these agree closely with experiment. Calculations can be performed on a computer, and a computer (in the abstract) is a classical system. So you have a classical model.

You can read more at http://quantropy.org/19/