Science papers are surprisingly conformist. If you want to get published, you do it the way everybody else does. If you want to push Bayesian analyses, you are probably better off doing it alongside p values, instead of as a replacement for them.

Do bear in mind, though, that p-values and ANOVAs aren't wrong. They're specialized tools that researchers tend to misuse. Having a Bayesian background should help you understand what they are and aren't suitable for.