The MW-Wilcoxon test is symmetric—deviations in mean ranks can occur in either direction in precisely the same magnitudes—and the distances of those deviations are mapped to specific probabilities, so I am pretty comfortable to that (Wellek gives an UMP formulation, but my formulation is simply TOST).

That said because the parameter of U is N units of U are pretty meaningless, so I direct software users and students to use units of the Z approximation instead for these tests (using the same logic as the last paragraph of the TOST tag info page). This raises again precisely your concerns about interpretation ("bad statistics"), but I think a thoughtful researcher can reasonably apply this.

Uh... rechecking Wellek... dang it, yer right, it is noncentral F. :)

"That said because the parameter of U is N[comma] units of U are pretty meaningless"