In a Japanse company I watch, they have a variant of the cage match where before escaping even becomes an option, you have to score a pin. And you can only escape by climbing out, the door is there to let wrestlers in only.
I like that stip since it freshens up the typical American cage stip. But that's just me. Not sure how an American audience would take to it.
I'd expect the American audience to take it really well. It makes sense and it's easy to explain.
Returning fans almost expect ridiculous stipulations going in with all the crazy matches from the Attitude Era. Fans who've been watching for a while see the current state of Cage matches and Russian Chain matches and the Chamber all the way up to shit like Dixieland, so by comparison this isn't that illogical. You've gotta beat your opponent in a regular match before you get a chance to leave outside the cage. Simple.
Hell, there's a bunch of TNA examples... if King of the Mountain can become a hit for wrestling fans, this is so much better than that lol