In an electrically powered A/C, electricity is used to compressed a gas. In the case of an aircraft, compressed gas is already available. Since what you need is a compressed gas to be cool, it is more efficient to just use the gas available. Energy conversions are wasteful. So it would not be a good idea to have the engines run generators (mechanical to electric conversion) then run an electric compressor (electric to mechanical conversion). It's a very elegant system. Also, the system is more simple because the electric motor (item that can break) is not present.
Currently I'm building my propane powered A/C in my basement, since I got interested in thermodynamics. Ok I have strange hobbies.
The new 787 somehow does not use air from the engines. I think many people are curious as to how they will get an energy saving this way. I certainly am.