I think Apple is more responsible. One of Flash's chief benefits to the customers who paid the big bucks was that it 'just worked' everywhere. Once Apple stopped supporting Flash on the iPhone, that story was a lot less attractive.

The bugs were definitely Adobe's fault: as with most tech companies, they were far more interested in expanding the feature set than they were on fixing the bugs and stabilizing the platform.

Flash was not particularly battery hungry (My go to example when HTML 5 demos started coming out was rebuilding a HTML 5 demo that was using 100% of 1 core into a flash app that used 5%).

The reason it burned CPU cycles is that non-coders could make programs with it and they would produce the world's worst code doing so that "worked". The runtime itself was fine (efficiency wise, not all the other things).