Analyzing papers in a glam journal for a year isn’t a very good way to judge what counts as science in terms of what is publishable. (“Just because it’s in Nature doesn’t mean it’s wrong!”)
That said, I agree that most of science is about becoming less wrong (choosing the least worst among available models for how observations arose), and that type of model selection problem is what Bayesian approaches excel at.
“Considering the evidence that preceded this study (or trial, or series), what explanatory model does the weight of the evidence best support?”
This need not be a binary decision (witness Bayes model averaging) and it need not be static (Bayesian updating explicitly evolves from a prior, whether flat or subjective). But it better matches the way most people approach research and probability, imho. Extraordinary claims must be supported by extraordinary weights of evidence, and frequentist testing in a vacuum doesn’t enforce this intuition.
Disclaimer: I am a statistician and a part-time Bayesian. Not a zealot, and not a jihadist against subjective inference. I use empirical Bayes procedures when they improve results on an ongoing basis, and I avoid them when the effort is more than the expected benefit can justify. The tipping point has moved over time, as more, faster, and better tools have decreased the cost (effort) to obtain a posterior distribution over complicated models.