No, I don't think it should be. A bit of experience in standing water with many auto tires convinces me that tread depth dominates, and that aquaplaning is not present with good tires at speeds much greater than predicted by the formula mentioned here which I recall the reference saying was determined experimentally. For an extreme example, a light racing car with tire pressures around 1 bar can obviously lap a wet track a whole lot faster than 35kts with wet tires fitted.
And on the other hand, with high quality tires almost worn to the legal limit (2/32nds inch tread depth) I've experienced aquaplaning at very, very low speeds on smooth surfaces. I've been convinced for a long time tires worn anywhere near the legal limit have no business on the roads.