I like the idea of the player who finished their turn choosing who goes next, that’s an interesting way to put pressure on people to take their turns instead of the group deciding who should go next with a big discussion.
I also incorporate a roll if a player wants to try and interrupt an action. If I say the NPC is going, and the player has a reasonable chance (story wise) of going first, I allow an initiative roll-off. Higher roll goes first. Personally I don’t use a ton of “punishment” mechanics if the players want to try something. My concern with your method is that some players would feel that risking having disadvantage on a save or something is risky enough to warrant avoiding your custom rule at all times. I’d say let them try to steal; if it works, great, and if they fail, then they have to be picked to go last in a round. That’s simple, and not too harsh, so players will more frequently take the risk.