I know that they cannot be local. My point of view is "just let them be global, build theories from there", global hidden variables don't interfere with any intuitions about the world for some reason.

The problem is you can't really build theories from global hidden variables. If the details of any experiment depend significantly\* on the state of the entire universe, until we can account for the entire universe in our measurements, we might as well stop measuring.

\* even with Newtonian physics, the universal attraction of any object does have non-0 values everywhere, but we know that the influence is negligible. However, with global hidden variables, the speed a billiard ball will take when I hit it may depend on the size of a planet in a different galactic cluster.

> If the details of any experiment depend significantly\* on the state of the entire universe, until we can account for the entire universe in our measurements, we might as well stop measuring.

Every experiment does depend on the entire state of the universe, even in QM, but those influences are typically small due to symmetries. At the quantum level, many of these symmetries no longer apply.

I also have a hard time disbelieving in global variables. We have a lot of evidence validating quantum field theories, and the fields in QFT are global.

Only in a trivial sense. Quantum Field theories are explicitly local theories, constructed from Langrangians which purposefully have and express Lorentz invariance, exactly to maintain locality.

In any case, quantum field theories are good at predicting stuff but almost certainly not descriptions of the true fundamental dynamics of the universe, given their known and relatively well understood divergences.