Maybe my example was contrived, but my main argument was that p-values represent P(D|H), or probability seeing your data conditioned on assuming that the hypothesis is correct, and that approach seems inherently flawed to me. If you're doing an experiment, p-values don't say anything about if the hypothesis is true or false, in fact the approach can't theoretically give that information. If you're doing a basic t-test, it goes something like this:

1. You have a null hypothesis you assume to be true

2. Based on this null hypothesis and the central limit theorem, if you theoretically conduct many experiments you expect some summary statistic to have a specific distribution around the 'true' population summary statistic and 'true' population variance, which you don't have so you assume it to be the null hypothesis

3. You compare your experiment's summary statistic to the hypothesized distribution. If the probability of seeing your summary statistic is below some threshold, you say it's unlikely to see this summary statistic again.

But the probability of seeing that summary statistic again actually depends on P(H), which NHST doesn't provide any information on. My examples were meant to highlight the nature of conditional probabilities, rather than how real life experiments are conducted.