It's a cert requirement that the aircraft be controllable after the loss of all engines. The 737 can be flown without hydraulics. The 747 (prior to the -8) requires hydraulics, but the windmilling engines will provide sufficient hydraulics to control the airplane in all engine out condition (as been demonstrated during a couple volcanic ash encounters) - when we went to the 747-8, the new wing required more hydraulic power to control, while the new engines windmilled at lower speeds and provide less hydraulic power, so the -8 got a RAT. The 757/767 required more hydraulic power than the windmilling engines would provide and got a RAT from day one.
Also, there is a cert requirement that electrical power can be supplied to the essential systems for at least 30 minutes after the loss of all electrical generation, hence the need for a big battery. In addition the 777 has a generator on the RAT (I'm thinking the 787 does as well but I'm not positive about that).
The problem after an all engine power loss (regardless of cause) is not that the airplane won't fly acceptably, it's that if you don't have an airport within gliding distance your chances of a happy outcome are not very good. The Gimli glider, Sully's miracle on the Hudson, the TACA 737 that landed on the dike, and the A330 that did a dead stick in the Azores all demonstrate the problem is not lack of hydraulics or electrics to control the aircraft, the real problem will be lack of thrust to get to a suitable spot to land.
I think that rather than invent a way to keep the APU running, the emphasis should be on preventing all engine power loss events.