It's not a really a choice in the Culture. There is zero chance of the Minds abdicating and submitting to human-only rule.

I doubt it would be a choice with AGI, and certainly not with ASI. It might seem like a choice, because true ASI would be persuasive enough to make it appear that way.

Discontent Culture factions do sometimes break away, though; if letting the minds do everything was unpopular, you'd expect the human population to drain away that way, but that mostly doesn't happen (main example would be the Gzilt, who never quite signed up in the first place).