That's a terrible example; Magic coat does nothing for espeon or its team. Quagsire does have a reason to clear stat boosts; for the rest of his team. For itself? No, you're right, Quagsire has no reason to use haze.Haze Quagsire is bad because Quagsire has Unaware, so it has no reason to clear opposing stat boosts. Even if Quagsire faints, most good stall teams have Unaware Clefable as well, so Haze isn't even useful in the event that Quagsire faints. It's like running Magic Coat Espeon.
And BP needs to have one specific Pokemon to be able to counter it, because "well-built teams" that do not use a hard counter auto-lose to it.
I get where you're coming from, and frankly having two or three "checks" (I wouldn't quite call them surefire counters as they really aren't.) that are viable in OU does not make a strategy healthy for the metagame. (Mega Lucario had plenty of counters, but he was unhealthy for the meta too since he trashed just about everything else. Same goes for Mega Gengar.)
You've convinced me; while I don't think BP deserves a full ban at all (it's a good move and interesting to use) I think the biggest issue here is Stored Power. Without stored power Espeon, while very strong, would not have the pure power it needs, as Unaware pokemon like Clefable and Quagsire could muscle through it.
I say that, if we ban anything, we ban Stored Power on Magic Bounce Espeon. Baton pass teams, while nerfed, can still function, have pokemon that can defeat it after it gets going (like any normal sweep thanks to stall and priority), but is still viable. And before anyone says it isn't:
Espeon can get past special walls with Psyshock, can crush things immune to its stab like TTar with Dazzling Gleam, and gan generally take multiple SE hits without going down. It's still viable, but more defeatable.
Of course, this is just in theory. This alone may ruin the entire thing. I don't know.