The problems with null hypothesis significant testing (NHST) are a direct result of two things:
1. the false air of objectivity it provides
2. the lack of consideration of the relative likelihood of the data under any alternative
I also agree that Pearson, Fisher, and Neyman knew what they were doing when they appealed to these methods' "objectivity" to support their terrible views.
I also find it just absolutely hilarious that Fisher's adamant opposition to Bayesian inference was the (in his opinion) absurdity of the uniform prior distribution, and yet one of his most famous contributions (Maximum likelihood estimation) is essentially the same result you'd get from the Bayesian estimate of the most likely parameter with a uniform prior.
If anyone is interested in the history of this stuff along with a discussion of the philosophical meaning of probability from the same author, his book Bernoulli's Fallacy is a pretty good read. My only qualm with it is the lack of much exposure on how to actually do Bayesian inference or a discussion on what it's like to do it in a modern setting. There's a brief few pages at the very end that mention things like Markov Chain Monte Carlo and the fact that most modern Bayesian inference is necessarily numerical approximations to the posterior, not the analytical solution (but that's not necessarily a bad thing nor is it an escape-able problem).
If you want a book that makes many of the same philosophical arguments about probability but also backs it up with math and descriptions on how to do Bayesian inference, Edwin Jaynes's Probability Theory: The Logic of Science is for you. It's quite literally a modern cult classic. People that read this book tend to go out and evangelize for it.
My final comment is that there is a place for frequentist methods, even if you're a modern Bayesian. The theory of Markov Chain Monte Carlo (one of the key methods in making modern Bayesian inference work) is exactly the domain of frequentist probability: Long runs of repeated things. Many of the diagnostic tools for assessing whether the inferences of MCMC results can be trusted are hinged on results from the frequentist interpretation and are steeped in their strange-ness. For instance, the lack of an issue is taken lack of evidence of an issue rather than evidence of no issue. The interconnected-ness of the two is unfortunately missing from the author's work (that I have seen).