Again: Priors can and are used to mislead. Both methods can and are used to mislead. Just moving to Bayes doesn't assume the finding is free of bias all of a sudden.
It doesn't. But the workflow of Bayes forces you be explicit. If you try and cook the books, it will be shown for the world to see. Can you provide a paper that quoted a p value for a regression and also validated all the asymptotic conditions are close to being true in order for that p value to be even somewhat reliable?