Would an auto turn feature...

Do you want to PLAY a game or RUN a simulation ?? I tried letting the ministers take over in one of my games when only an AI neutral was left in one system (set as systems to avoid and no AI politics/attack). I wanted all the planets colonized to get my racial points up, but did not want to spend a week doing all the micro management. It ran a couple of turns then locked up. Interrupt showed as SE IV task not responding. So I guess if you have a big (>300-500 colonies) empire the AI chokes on it anyway.