I don't even get what the conflict is between Bayesian and Frequentist statistics. Too me it seems like Bayesian statistics is useful for some set of use cases,

I don't even get what the conflict is between Bayesian and Frequentist statistics. Too me it seems like Bayesian statistics is useful for some set of use cases, and frequentist statistics for another set. Frequentist hypothesis testing falls somewhere in the middle, and as long as it's not over-interpreted is fine as it is, with the advantage being it's easy to do. Though the downside is that it's not easy to interpret. The downside of Bayesian statistics, in my experience, is that it's really hard to teach it to less-than-very-bright people, even in the academy. I mean, those who don't even understand what "falsifying a null-hypothesis" means (and doesn't mean) will have a very hard time doing Bayesian analysis properly. In a more advanced setting, though, Bayesian approaches provide a much better tool for comparing a set of alternative hypotheses. But it requires that users understand the math, and are not just following some script, and also that those involved are willing to provide their priors before evaluating the data.