In space, you'd be rotating in many directions quite often making it very odd to try and aim at something.
True that, but I'm sure this could be alleviated. For example, auto-rotate your POV to hold it more stable when the ship turns/rolls, have an indicator on the edge of your view port showing where your target is if it's off screen, perhaps have a slight "homing effect" for your aim when you're pointing close enough to the target, etc. Yes, not easy to implement, would probably take a lot of testing to get the controls "right".
Or, simplify it a lot: have the turret auto-aim at your chosen target, but drift off when the ship makes sudden movements - basically only leave corrective movements and timing of fire to the player?
Well, can't say how well these would work without experimentation - who knows, maybe FDev
did experiment with this but ditched the idea when it didn't work out?
But I certainly like the idea, especially for multicrew (if it only worked better!). I've even entertained the idea of dirt cheap "pleb level account" that would only allow you to play CQC (because I've heard it's pretty dead there) and crew other players' ships. This would be a good way to introduce people to the game or have your kids play with you even if they're too young or uninterested to have the full Elite experience. Heck, FDev could even have promotional "free weekends" allowing people to try the pleb account for free to lure in more potential players.