When it looks right, it will be right. When it is measured looking right, it will be found that the square root formula has been agreed with.
What you can not scale is the reaction of the water in forming those nice creamy wakes. That depends on the surface tension of the water, and that remains constant, so whatever bubbles form are always the same size.
One thing that is useful is using a cube root formula to guess at the power needed. Important factors there are trusting the quoted figures for the ship in question (naval authorities are known to sometimes be economical with the truth when state secrets are involved), then knowing that there is a difference between power output (full size) and power input (to a model motor) and the efficiency difference between getting the power into the water. Since they need sea trials to find out if the real thing lives up to expectations, there should be no surprise when it happens that there is a measure of guesswork in the model world. TLAR gets used a lot, as does TSAR.