I don't really see Frequentism and Bayes to be in conflict. You use them to answer different questions. I wouldn't test a point null hypothesis with a Bayesian model.
I think the Bayesians argue that you would, so there does seem to be a conflict.
I think most Bayesians would claim that point null hypothesis tests are immoral or something like that, rather than propose to do them with a Bayesian model (thus avoiding measure zero problems)
It honestly just seems like an abstract debate to claim that your logical framework is somehow superior. Different tools for different datasets