My favorite was the fiscal corporal from DFAS Kansas City who was in my SERE class as a "reward" for Marine of the Quarter or something. I totally thought, "WTF?"
Airborne training is a gimme. Marginal cost is almost zero, and the Army trains so many more than will ever conceivably jump into battle, that it's more of a motivational or confidence-building tool than anything else. Our SgtMaj has passed that Marines who ask for that in their reenlistment papers will likely get it honored.
Dive training is specialized and higher risk. It would be a travesty for anyone not requiring it to go. ESPECIALLY an aviator or prospective aviator--barotrauma, anyone? ANGLICO used to send a lot of their personnel to dive training, but I think that's tapered off.
SCUBA as an insertion technique is such a corner case as to be almost silly. Hydrographic reconnaisance is probably one of its few combat roles.