If a competition has divisions based on the break timing, then I don't see any problem with Colombians, Cuban style dancers, etc., picking one of the timings and entering in the event. LA style dancers competing in the on2 division? Why not, as long as they can keep to the on2 timing throughout their routines. On1 doesn't have to mean LA style, and there's no reason why "on2" has to be NY style ET2.
One alternative would be to have style-based divisions in a competition, e.g., LA on1, NY ET2, Cali style, Casino, etc., etc. - but where does that stop? Where do Power2 competitors go, for example? Should you have separate categories for Cuban and Miami styles? Should London style dancers be allowed to compete both in on1/on2, stick to one or have their own London style on1/on2 division?
Another alternative, obviously, is not to have divisions at all (other than "pair" or "group" perhaps). I don't see any problem with this either (though it may be difficult for the judges).