It is a common technique in diving however I wonder if there are different reasons why it is so effective.
Diving often involves a degree of excitement, panic or a combination of both! Perhaps just like flying! So the diver breathes more rapidly (and even hyper ventilates). Breathing more rapidly simply means the air is gulped from the demand valve and not used efficiently. Hyper ventilation is a great deal more serious because it suppresses the normal level of C02 in the blood and counter intuitively constricts the blood vessels interfering with the transport of oxygen - all bad. (Pace I know you know this)
As we have rehearsed and in contrast at altitude the lungs gradually diminish in their ability to transfer oxygen; I dont see by holding the air in the lungs this will change anything. It is not that the pilot is trying to conserve air, after all it is not that it is in short supply, rather there is not enough oxygen in the air relative to the ambient pressure. Breathing rapidly clearly will make matters worse, and I would guess holding each breath a little longer might mean the oxygen available is better absorbed, but I would guess the difference is negligible. Pressurising the air clearly is beneficial but as the discussion has flowed it would seem this is very difficult to do in a controllable and meaningful way.
I still reckon fitness is the simplest way of improving matters. There is no doubt the fitter you are the more effective your lungs are at absorbing what oxygen is available and the better the body is at transporting the gases around the body (with the caveat as we have discussed that fittness and altitude resilience dont necessarily go hand in hand). I reckon if you want to operate at higher altitudes without oxygen get your weight down to recommended levels, do lots of aerobic exercise and of course quit smoking (if you do).