If it weren't for the randomness of measurement results

Yeah. For the third time now at least, I repeat that Bell's theorem is also violated in a fully deterministic, or indeed superdeterministic world which isn't at all random.

and without making the assumptions plausible, there is no constraint to be violated

Agreed.

In practice we have significantly more information than just the minimal framework of a Bell test to work with

I agree largely, and of course: all of what we measured and seen so far in QM experiments points us towards QM being correct and complete.

However, if that's the argument, then why bother violating Bell's theorem at all? And if one—and again, that's a big if that you don't have to subscribe to, as I've said many times now—wants to bother with it, then no amount of "yes, but in other experiments..." will help you circumvent loopholes especially when they are of a nature that render your experiment incapable of distinguishing between local and nonlocal theories.

Until it is your problem I don't see why anyone should take LHV's seriously.

I can only repeat, again, that I'm not saying that LHVs are reasonable, and that it's fine for you to not care about them. My argument is on violations of Bell's inequality, and not on the reasonableness of LHVs.

Btw., are you aware that hidden variables are well and truly alive even forgetting about loopholes for the moment? It seems to me that you strongly reject the notion of hidden variables per se, local or not.

Then why are they interesting?

Again, my argument was not about that but about a violation of Bell's inequality. But ok, why are they interesting? Because they are a plausible model of what we see in experiments. They cannot even be ruled out once we have an actual Bell inequality violation, with all loopholes closed.

Because as I said earlier, you can still have LHVs if determinism or superdeterminism holds, or indeed if any of the many other implicit assumptions of Bell's theorem happens to fail, e.g. Minkowski spacetime, directed causality, probability theory, etc.

Is local realism more valuable that a theory's reasonableness for some reason?

This whole discussion started in 1935, with people like Albert Einstein saying that the theory wasn't reasonable. Many very clever people who thought about this for decades still share his view even today. I think it's a bit presumptuous (at least for me) to dismiss their concerns despite the fact that 7 decades later, and the fact that we're starting to build quantum computers, we haven't even managed to properly do a Bell experiment yet.