As for dragon age it was default, where you'd set the AI to react in a certain manner to specific triggers/circumstances.
No, there was specifically a mod for DA that let you enable your currently "controlled" character to act on the AI you set up. I used it myself from time to time, particularly when I had to take a phone call or something.
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Having such a mod for XCOM sounds like a neat thing. I, too, occasionally enjoy the idea of managing things before the battle but then having your soldiers taking their own initiatives rather than being meticulously guided by some eye in the sky. Maybe even have some sort of intelligence value so that more intelligent and/or experienced soldiers make better and less risky judgment calls. Maybe use Will as a basis?
I would like some form of toggle in-game for it though, so I can choose whether to use the AI or guide them myself - but not so freely accessible that I can let the AI handle just some soldiers. Maybe having it toggle on a per-mission basis.