To what extent does the industry use Bayesian methods? It seems to me that, for a given trading strategy, trading companies are really interested in the mean profit impact of the strategy and its distribution (e.g. "there is a 10% change we will lose more than $20M"). Bayesian methods will naturally produce such an answer.

Bayesian methods won't magically solve all problems (e.g. fitting to historical data) but could make the assumptions more clear.