Do you take issue with the 'purely empirical' approach (just trying out variants and seeing which sticks) or only with its insufficient documentation?

I don't know how you'd improve on the former. For a lot of it there simply isn't any sound theoretical foundation, so you just end up with flimsy post-hoc rationalizations.

While I agree that it's unfortunate that people often just present magic numbers without explaining where they come from, in my experience providing documentation for how one arrives at these often enough gets punished because it draws more attention to them. That is, reviewers will e.g. complain about preliminary experiments, asking for theoretical analysis or question why only certain variants were tried, whereas magic numbers are just kind of accepted.