I'd argue that p(H0|x) is also (in most cases) pretty uninteresting from a scientific perspective, and so the whole "publish all the p-values" solution I think

I'd argue that p(H0|x) is also (in most cases) pretty uninteresting from a scientific perspective, and so the whole "publish all the p-values" solution I think is only fighting half the battle. Gelman does a much better job of arguing this than I ever could [1], but this idea that rejecting the null is the "desired" outcome is the real problem. To put it another way, a low p-value is another way of saying "my model of the data generating process is bad", which is in most cases a pretty unsatisfactory outcome. As to the idea that priors are "impossible" to get, to quote Gelman [2] again, why "strain at the gnat that is the prior and swallow the ungainly camel that is the iid likelihood? [1] https://statmodeling.stat.columbia.edu/2015/03/02/what-hypothesis-testing-is-all-about-hint-its-not-what-you-think/ https://statmodeling.stat.columbia.edu/2015/03/02/what-hypot... [2] https://statmodeling.stat.columbia.edu/2015/07/03/why-should-anyone-believe-that-why-does-it-make-sense-to-model-a-series-of-astronomical-events-as-though-they-were-spins-of-a-roulette-wheel-in-vegas/ https://statmodeling.stat.columbia.edu/2015/07/03/why-should...