I'm personally pretty comfortable with such "pre-data" guarantees as long as they're sufficiently high probability (e.g. if they hold with probability 99.9999%, I'm not too concerned that I might be unlucky for this specific interval). But I'm not necessarily that interested in defending p-values. I don't dislike them, and I think they can be quite useful in some situations, but they're not the best thing ever.

I do, however, think that concentration bounds are really good, which I would consider to be a sort of conceptual descendant of p-values (but I have no idea if that's actually how they were developed historically).