I think we agree on NHST. I expend a lot of effort to remind students (and colleagues) that the popular interpretation of significance tests gets the direction of implication backwards.
Why do I care about the properties of my test if it doesn't say anything about the what I should know about the thing I'm measuring in this specific case. Covering the true parameter 95% of the time is useless if I can't make that leap to saying this one contains it 95% of the time.
It's so confusing, and I say this as someone who has devoted all of their adult life to statistics.