I've had this idea before. What if it instead changed everyone's controller ports, making you control another person's character for the duration he's out? It'd make everyone play like an absolute backwards mess. People attempting to run off the stage to kill the character they got control of. People attacking their own character just to keep them from SDing, but trying to keep the damage minimal at the same time. In teams or FFA's, throwing out risky moves to try and get a lucky kill or stupid high damage with no care for how safe it is because the damage they take isn't there's, but at the same time, people will try to direct the character they got control of into their own character's attacks, so you still have to avoid killing the real you. They'd have to juggle all the pros and cons to just SDing, keeping their own character alive, and killing other characters in the lead. I'd say there'd also be the side effect of losing respawn invincibility to avoid making things too easy.
It might even make weird team up scenarios, like if you end up controlling your own teammate, but your teammate gets control of an enemy. Then you'd be protecting your teammate from being protected, making sure nobody gets in the way of him SDing. And of course, getting control of your teammate's Ness while your teammate gets the enemy's ZSS, and then you get your teammate to heal his character with the enemy's attacks.
It could also swap the ports of people who have already lost all their stocks, letting that player wreak havoc since absolutely nothing matters to him with his character dead, and the person who got the dead character's port has to just wait it out. It would give them a chance to revenge kill somebody from the dead.
Everyone would be fighting in complete chaos. It's all pretty fitting to Mantis' mind control and 4th wall breaking shenanigans.