The main use of non-locality I've seen is in relation to (fused) anyons carrying quantum numbers held non-locally over their constituent parts. I expect we see other non-local effects in things like very low temperature condensates and probably stuff like superconductors and superfluids (since the math of the vortex structure is similar to anyons).

Of course, entanglement can be interpreted as non-locality, where what happens to one particle inside of a bounded area depends on the fate of its entangled partner, outside of the box.

The real reason to use non-locality in place of indeterminism is that it provides a clear research avenue to combine the QM effects (based on information locality) with GR (which is about the causal relations between things). QM would really just be telling us that the actual causal net doesn't look like it does from macro scale. It transitions both frameworks to be about causal nets, instead of a weird mishmash that's hard to combine.

Of course, that's if we can do QM as pure non-locality, rather than indeterminism. I just think it's strange that it seemingly hasn't been investigated.

Ed: I guess it has been investigated some by say, Bohm, but I feel like science (the institution) gives undue weight to the interpretation they were taught in school, even when it's both arbitrary and constraining. It's like everyone screaming that of course there's exactly one parallel line, that's what you're taught in school and have been since the Greeks, right? Well, maybe non-Euclidean geometry models some things better.

Similarly, I think scientists baked some arbitrary design and philosophy choices in early, then never bothered to explore other approaches, because they were able to compute decent results.