Your thinking that all out of air problems are coming from divers just staying down till they are out, I would say that most of those stats are also from going places they should not or aren’t trained for such as wrecks and caves. The OOA are trained for the unforseen issues also such as o-ring pops, hose ruptures, free flow at depth, and will run out before reaching the surface.
If you don’t train the student how to handle OOA situations then they won’t know what to do if they ever have something like this happen to them.
Saving the training for a later classes is assuming they take another class, since they are free to dive after training i think passing up life saving skills would not be in the best interest of the student.