I suggest looking at the essay "Beyond Bayesians and Frequentists" by Jacob Steinhardt http://cs.stanford.edu/~jsteinhardt/stats-essay.pdf , who says, "The essential difference between Bayesian and frequentist decision theory is that Bayes makes the additional assumption of a prior... and optimizes for average-case performance rather than worst-case performance. It follows, then, that Bayes is the superior method whenever we can obtain a good prior and when good average-case performance is sufficient. However, if we have no way of obtaining a good prior, or when we need guaranteed performance, frequentist methods are the way to go." The same author also has an essay that tries to explain why Bayesians shouldn't be so confident in their approach: "A Fervent Defense of Frequentist Statistics", 18th Feb 2014, https://www.lesswrong.com/posts/KdwP5i6N4E4q6BGkr/a-fervent-... Note that the author isn't against Bayesian approaches, but against the dogmatic assumption that frequentist approaches are always worse.

This is nonsense. Nothing stops a Bayesian from picking a prior that optimizes for worst-case rather than average-case performance, given a particular utility function. The really questionable premise here is that the utility function is known; in practically any case of real interest, it isn't, and that's a problem regardless of whether your decision theory is "Bayesian" or "frequentist" (which are misnomers for decision theories anyway for the reasons I gave in my other post just now).

This essay is about decision theory, and the things he is calling "Bayesian" and "frequentist" are more than just statistical methods, which is what the replication crisis is about. Decision theory, particularly when other agents are present, cannot be handled by any method that only considers statistics; game theory is involved. The Steinhardt article is basically claiming that "Bayesians" can't use game theory while "frequentists" can, which is nonsense.