> Our observation of a loophole-free
Bell inequality violation thus rules out all local realist theories that accept that the number generators timely produce a free random bit and that the outputs are final once recorded in the electronics.
Why should a local realist theory accept that? In determinism, there are no random events.
This has been studied. The kind of determinism that a local realistic theory requires in order to explain Bell violations is generally regarded as absurd: https://en.wikipedia.org/wiki/Superdeterminism
But that is just regular determinism; everything is determined by the prior state of the system, including the operation of the number generator and the experimenter's movements. As far as physics models go, I cannot see anything absurd about it.
"Regular" determinism doesn't necessarily affect Bell's Theorem. All you need is that the measurement choices at each end are "effectively free for the purpose at hand". The kind of determinism you'd need to actually affect Bell's Theorem is a pathological, conspiratorial one in which the universe is well aware of which measurement choices you are going to make and just sets things up so that you'll get the same outcomes that quantum theory predicts.
Why should a local realist theory accept that? In determinism, there are no random events.