I don't think the net effect of a mass switch to Bayesian methods would be negative, but I do think it'd be very small unless it involved raising the general statistical competence of scientists.

I think that teaching Bayesian methods would itself raise the general statistical competence of scientists as a side effect, among other things because the meaning of p-values is seriously counter-intuitive (so more scientists would actually grok Bayesian statistics in such a world than actually grok frequentist statistics right now).