This is beginning to make sense to me. It would prevent Box being able to use assimilation during his turn and then again from mind control during a multiplayer match to beef him up to face a third opponent, or to get him to heal out of being a giant. I can actually think of some times when you would want to do this to him.

Possession seems to be the reason why it's stated "once per round" I've often hated to face Box when he's Thunderbolted to X-Men.

Sorry to butt in, guys, but to me the explanation would really only come down to this:

and maybe this:

That aside, I also think it's just a case of another bad wording. Instead of "once per round", it should rather say "once during your turn".

Now that I think of it, the Cuckoo's Hive Mind SP is also poorly worded, and that was in the same set as Box!
Since it says 'end of the round' it matters a lot whether you go first or second in the game: If you go first, you have the bonus until your opponent has had a turn, if you go second, you only get the bonus during your own turn - after your turn the round is over.
At my venue we quickly house ruled the power to read "until the beginning of your next turn" instead to keep things simpler.

Yeah, before the FF rules set, Cuckoo's were frequently thumbing their noses at Perplex characters

And now it's the other way around...