[EDIT: I realize this question is soft. I realize some people want to close this question. The goal here is trying to answer the following question:
So I see these research papers that provide papers for oracles B s.t. C^B != D^B.
Question: How do I build on these results? [Besides proving other oracles?] Are there examples where people have techniques that utilize oracle separations? ]
For many classes C, D we do not know about C vs D, but we have oracles relative to which C^A = D^A, C^B != D^B.
Is there any class separation result that has been inspired by Oracles? I.e. the argument is that finding such oracles shows that these classes are "hard to separate", -- but does having examples of separating oracles actually help separate the class?
Is there any case where the existence of a B s.t. C^B != D^B somehow guided the proof of C != D ?