Rayquaza and Giratina also didn't appear on a cover when they were first introduced. For the record, I'm not trying to claim that Hoopa was/is broken as those three, just that "it isn't on the cover lol" doesn't seem a very scientific criterion and it almost feels like AM was shitposting.
I was actually being serious. This has been "consistent" since at least Gen 2 with introduction of Ho-Oh and Lugia. Mewtwo was an exception because those games were based on a color scheme for Pokemon Red and Blue to start the franchise off, Pokemon Yellow putting emphasis on the Trainer Red and Pikachu relationship, at least in America. Rayquaza is an exception to this because Ruby and Sapphire represented Groudon and Kyogre for again color schemes, this also ends up with Rayquaza for the Emerald cover a couple of years later anyways. Same deal with Diamond and Pearl, Dialga and Palkia. The 680 BST philosophy is more of a coincidence when applying to bans because Gamefreak intentionally places a BST value to give importance or certain attributes to certain mons, with 680 being a standard for big legendaries, 600 BST for psuedo-legendaries like Tyranitar, and so forth.
To be fair the specific criteria is more or less what Selhido pointed out. There's no politically correct great term to phrase it other than that and it's easier to just ban from that angle in most cases. The confusion comes from the fact we're starting to hit generations with all sorts of weird shit such as mid battle evolutions, alternate forms of mons that exceed or break the usual philosophy of cover legend bans, and mons like Marshadow who don't have the highest of BSTs but other attributes push it beyond the scope of being healthy. Those are usually taken care of through the usual suspect process, in this case Hoopa-U was like this.