It appears to me that the Kochen-Specker theorem, if not Gleason’s theorem already, seals the fate of realism / value definiteness (with possibly the additional assumption of non-contextuality, depending on how one precisely defines the above terms). Unlike Bell's theorem (though like some of what is commonly considered within Bell-type inequality offshoots such as CHSH Inequality) the Kochen-Specker theorem appears to clarify the line between classical and quantum, when one finally has to accept that quantum cannot be imagined apart on the boundary (Hilbert space / measurement).
Bell's theorem in itself, on the other hand, does not appear the resolve clearly (I am speaking for myself) which of the components of the local realism is wrong if the inequality is violated (locality or realism or both). Yet, for some reason, it appears that the Bell's Theorem has garnered far more fascination among the physics community. (Q1) Is it because of the appearance of the faster-than-light communication, or this is just a historical accident, helped by the fame of the EPR paradox?
On the basis of (numerous) experimental evidence, we know that we need to deny its premises, namely, either (or both) of the locality or realism (that many physicists will argue had known always to be true, even without any experimental evidence). Logically, in itself, this may convey the idea that it is possible to have non-locality (with realism in place).
(Q2) However, since we already know (e.g., by the Kochen-Specker, etc) that the realism assumption is incorrect, then the Bell's theorem per se does not appear to resolve the validity of locality vs non-locality assumption?
In fact, it appears to me that the experimental evidence (that shows the violation of the inequality) may be safely interpreted only to confirm the invalidity of the assumption of realism. Further confusion may be introduced when one understands (or, so it seems) that the locality in the Bell's theorem or Bell-type family of statements -- at least those that I have seen -- is defined and intrinsically linked with the realism assumption so much so that it may at least be profoundly misleading to state that one can dispose of realism whilst retaining locality; it is not clear (to me) what kind of notion of locality it would be. To the extent that it is the idea of locality intrinsically linked with realism (value definiteness), then the Bell's theorem does not appear to imply anything about it (fortunately, relativity makes it clear); and to the extent that it is some other notion of locality, then it appears it could be anything, including some type of quantum locality that, when represented in our standard spacetime, are actually quite non-local (but, of course, due to absence of realism or value definiteness, it cannot be used to deterministically send signals faster than light).