You only stop a play on a timeout on your own possession.
A challenge system, by its very nature, would involve stopping play whenver/wherever a bad call was made, or in the laternative, stopping it on your own possession, and then going back and changing something that had already happened earlier and having to replay from that point. Neither is sensical, nor so far as I know has ANY league in ANY continuous play sport EVER instituted such a ridiculous device. Its just not that big of a deal, and if the games are reffed properly in the first place, the bad calls more or less balance. Only in the case of biad are they likely to pile up and become decisive against one team, and if you have such a bias involved, you aren't going to stop it with challenges, nor is there any rational way you could give a coach on the wrong end of a fix enough challenges to matter. What, is Rick going to get to stop the game a dozen times in the 4th quarter of game 6?
The answer does not lie in screwing up the very flow of the game that makes basketball attractive just to get the occasional call corrected. It lies at a higher level of referee oversight and control.