The question assumes hat a $b$-bit preimage attack randomly produces b bit preimages. This is not a realistic assumption.

We could imagine a $b$-bit preimage oracle which deterministically produces just a single $b$-bit preimage - never more never less. Running it multiple times will not give us any additional advantage than running it the first time.

Access to a partial preimage oracle does not seem to help at all in solving the full preimage problem.