This is closely related to my PhD. It was many years ago but if I remember rightly there is no need for the assumption of determinism - Bell Inequalities hold just as well for random local hidden variables.
Simulating the correlations with computer programs is an interesting idea, partly because it challenges to those who still believe in a "local" reality to demonstrate Bell Inequality violations in distributed classical computer systems. Back in the day there was a crackpot researcher named Joy Christian who kept publishing repetitive papers in the belief that geometric algebras provided a counterexample (it looks like he's still going strong! [0]). Of course, there's nothing about geometric algebras that cannot be modelled in a computer program, so in principle Christian should have been able to demonstrate Bell violations in a distributed scenario. Needless to say, this hasn't happened even though it would be a momentous breakthrough in the foundations of physics.
Simulating the correlations with computer programs is an interesting idea, partly because it challenges to those who still believe in a "local" reality to demonstrate Bell Inequality violations in distributed classical computer systems. Back in the day there was a crackpot researcher named Joy Christian who kept publishing repetitive papers in the belief that geometric algebras provided a counterexample (it looks like he's still going strong! [0]). Of course, there's nothing about geometric algebras that cannot be modelled in a computer program, so in principle Christian should have been able to demonstrate Bell violations in a distributed scenario. Needless to say, this hasn't happened even though it would be a momentous breakthrough in the foundations of physics.
[0] https://ieeexplore.ieee.org/document/9693502