Why are Oracle Separations Counted as Evidence toward Unconditional Separation? Particularly, we already have some oracle separation results such as $\mathbf{BPP}^A\neq \mathbf{BQP}^A$ [Simon], $\mathbf{NP}^A\not\subseteq \mathbf{BQP}^A$ [BBBV], and $\mathbf{BQP}^A\not\subseteq \mathbf{NP}^A$ [Bernstein and Vazirani]. But given that most problems are non-relativising, how does such oracle separation even counted as evidence of unconditional separation? Or do we need to discuss it case-wisely?
At best, the evidence given is only heuristic and informal, but it is still important. Oracles in the examples you gave do address the general question: how does quantum computing compare to nondeterminism and randomness, in power? The oracles definitely do not answer the original unrelativized questions, rather they provide a different (related) black-box model where the question provably has a negative answer. Since unconditional lower bounds are very difficult to come by, oracles can be useful information, but again it's only heuristic.