Is the purpose of Stage 2 clutch and tranny kits so that you can powershift without the threat of damage to them? This is what my muscle friends have told me.

Your friends have no idea what they are talking about. Stage 2 clutch (and any performance clutch) goal is to not slip under higher than standard clutch load. Lets say you get to put a turbo on your car, and leave clutch stock. Now the stock pressure plate does not have enough power to press the clutch disk against the flywheel hard enough for it not to slip, also stock clutch disc does not produce enough grip on the flywheel not to slip, so as a result - clutch will start slipping and burning, eventually failing (pretty soon).
Gearbox reinforced internals are used in the same way, but when a stock gearbox fails it is usually because the gears inside it can’t hold the new stress of upgraded power and sheer their teeth, so a reinforced set of gears is required. Powershifting is damaging on any drivetrain, due to the fact that it’s a violent shock, not due to the fact that "there is too much power". I should know, I’ve powershifted and clutch kicked myself straight to a full transmission replacement, now with heavily upgraded clutch and differential.