Remember, too, that only Dr. Strange could've kept Quill from going nuts. Tony tried, but he was destined to fail.
At least that's how I figure, since only Strange himself could bring about any of those alternate futures. He's like Bill Murray in "Groundhog Day." There'd be no point exploring futures beyond Strange's own control.
So that means, to me, that only Strange could've prevented Quill from blowing the deal. And in many of those alternate futures, he probably tried and maybe even succeeded at keeping Quill calm enough for them to remove the gauntlet.
My guess is, in those futures, Thanos either gets it back right away or even years later. He's clearly very hard to kill and functionally immortal. Perhaps there were futures where the Avengers win, only to have Thanos return a century or two after they're nearly all dead.
Instead, Dr. Strange guided them to the one future where Thanos is decisively defeated and the stones are removed entirely from temptation. Unfortunately, that future required Tony to die, which meant that Tony had to survive on Titan.
So he let Thanos have the gauntlet back, and let him have the time stone, all so Strange could extract Thanos's promise NOT to kill Tony Stark.