Bell's theorem - for or against Hidden Variables?

[gill1109]

"In real Bell-CHSH experiments, we can't observe quadruples (A, A', B, B'). It is only the hypothesis of local realism that says that they do exist."

Exactly!  You have a hypothesis that is physically impossible to test.  So it is junk science to think that the experiments are testing the hypothesis.  They aren't.  They are only confirming that the predictions of QM are correct.  Which is good.

Under the hypothesis of local realism, Bell's inequality follows; and it is possible to test, up to statistical error and statistical uncertainty, whether or not Bell's inequality holds.

The hypothesis of local realism has observable consequences.