Hybrid actually makes a lot of sense for aircraft. As you yourself mentioned, you're carrying around a heavy cast metal thing for 100% power output when you in fact only use 70% of the power for 99% of your flight. So you lug around all that dead weight just to be able to provide you with enough power for takeoff that you don't use after that.
Wouldn't it be better if you could have a smaller APU that could provide the cruise powering, and leave takeoff to a much more efficient electric motor?
It could be a turbine APU, like the passenger jets have - even more weight savings. And say goodbye to the hassles of 100LL at the same time.
Also, there is regenerative opportunities in aviation, although perhaps for smaller spamcans maybe less so.
The flat power/torque curve of electric motors means you can get rid of the complexities of constant speed props and tons of other equipment that todays aircraft are saddled with. Starters, generators etc. The weight savings are huge.