Bell's theorem rules out theories of local hidden variables. It says nothing about non-local hidden variables, or even something more mundane like determinism (sometimes referred to as "superdeterminism").
In any case, I'm not sure Bell's theorem has much impact on my question: why is one of these things (transfer of information from a coin toss) not a problem, conceptually; whilst the other (entanglement of quantum systems) is a problem, conceptually?
(Personally, I don't find either particularly troubling; just curious to know what the philosophical distinction is, without appeals to "quantum weirdness")
Yet entanglement is observed non-locally, even backwards in time or between degrees of freedom that never co-exist. Nobody has been able to create a non-local model that doesn't require fine tuning and the idea goes against the spirit of special relativity.
Thus, I would agree with you, there is no "problem" with entanglement. Except non-locality.
Is this scenario fundamentally different than the quantum system? Is this scenarion also a "problem"?