I'm not sure I understand your reasoning regarding the price of bitcoin staying the same and the miners having an incentive to double their hashpower. In the situation you described, you'd have the same hashing power but half the energy cost? Doubling it would double their hashing power and keep the energy cost the same. I don't see how this doesn't lead to a more secure network?

I don't think you can neglect the price of a new ASIC in a real situation though, those things are very expensive. Where it was first possible to attack the network using regular hardware, it now requires a much bigger capital investment. When ASICs were first released they had a bigger advantage than they have now, it seems unlikely a 2x improvement over the previous generation is still possible (assuming it was possible before, I didn't check).