> The article is all about why "0.05" might be a bad value to choose.
No. It's more about why choosing a value to serve as the default choice is a bad idea in the first place. The specific value chosen as the default itself (i.e., 0.05 in this case) is irrelevant.
The idea is that the value you choose should reflect some prior knowledge about the problem. Therefore choosing 5% all the time would be somewhat analogous to a bayesian choosing a specific default gaussian as their prior: it defeats the point of choosing a prior, and it's actively harmful if it sabotages what you should actually be using as a prior, because it's not even uninformative, it's a highly opinionated prior instead.
As for points 1 to 3, technically I agree, but there's a lot of misdirection involved.
The point on effect sizes is true (and indeed something many people get wrong), but it is contrived to make effect sizes more useful than p-values. In which case, the obvious answer is, you should be choosing an example where reporting a p-value is more important than an effect size. One way to look at a p-value is as a ranking, which would be useful for comparing between effect sizes of incomparable units. Is a student with a 19/20 grade from a european school better than an american student with a 4.6 GPA? Reducing the compatibility scores to rankings, can help you compare these two effect sizes immediately.
Prior probability, similarly. "If" you interpret things as you did, then yes, p-values suck. But you're not supposed to. What the p-value tells you is "the data and model are 'this much' compatible". It's up to you then to say "and therefore" vs "must have been an atypical sample". In other words, there is still space for a prior here. And in theory, you are free to repurpose the compatibility score of a p-value to introduce this prior directly (though nobody does this in practice).
Regarding p=0.05 vs p=0.001 not mattering; of course they do. But only if they're used as compatibility rankings as opposed to decision thresholds. If you compare two models, and one has p=0.05 and the other has p=0.001, this tells you two things: a) they are both very incompatible with the data, b) the latter is a lot more incompatible than the former. The problem is not that people use p-values, the problem that people abuse them, to make decisions that are not necessarily crisply supported by the p-values used to push them. But this could be said of any metric. I have actively seen people propose "deciding in favour of a model if the Bayes Factor is > 3". This is exactly the same faulty logic, and the fact that BF is somehow "bayesian" won't protect subsequent researchers who use this heuristic from entering a new reproducibility crisis.