I have done a bit more reflection on the matter, and I still haven't seen any non-aesthetic argument offered here. I am in complete agreement with most respondents in this thread that being required to nickname your Pokemon to avoid a potential information leak is a dumb mechanic (since it's optimal to at least bluff you have Beat Up). However, an argument from purely aesthetics feels very, very weak to me. It's like saying "we should allow Shiny Greninja to have Battle Bond because Shiny Ash-Gren looks epic. Shininess doesn't impact play either, so there's no downside!". I think Shiny Greninja is way cooler than non-Shiny, but I hope everyone would agree that intentionally breaking set legality to allow for aesthetics would be an unwarranted deviation from cartridge.
I assume people are memeing about the "nickname all your Pokemon another mon's name", but I'd be perfectly fine with that as a solution. That clause is just inherited from VGC play, and there's no reason OU has to follow it. So that'd be a perfectly fine change that wouldn't break cart mechanics at all, and because it'd be even possible to nickname your Pokemon another name, it removes the obligation to nickname all mons 1 2 3 4 5 6. So that sounds fine to be, but I assuming those suggestions are less serious.
I don't find Hipmonlee's differentiation between modifying the playing conditions and modifying the mechanics very helpful. You might be able to distinguish between cart-possible convenience features and not cart-possible convenience features. For example, it's certainly possible to track PP usage yourself, and you could keep detailed logs. A neutral judge could enforce a move timer as well. On the other hand, something like 'Cancel Mod' is a not cart-possible convenience feature, modifying mechanics, and defined as such in
all official formats. We have to implement special logic for Imprison so the Cancel button doesn't leak information about what moves the opposing Pokemon could have, for example. So I don't find the distinction relevant to the discussion at hand.
However, I do think Hipmonlee is on the right track towards a plausible argument that respects cartridge. Unlike in modern gens, if you have your Pokemon nicknamed, there's no way to actually pull up the Pokemon's name if you don't happen to recognize the sprite. You could see the sprite of Tyranitar, but you wouldn't necessarily know its name was Tyranitar. So maybe you have some helpful, neutral judge who informs the player about the name of the Pokemon they're fighting if they are unaware. So let's extend that to nicknames! Suppose each player nicknames their Pokemon all the same name, but you give this neutral judge
another list of nicknames that they announce whenever your Pokemon does something identifiable, like switch in or faint. So if you lead your Tyranitar, with the name 'A' on cart, the neutral judge can say "Player 1's Tyranitar's extra nickname is Despotar" or something similar. Then, when you use Beat Up, it just says "A's Attack!" 6 times. Showdown's nicknames here would be more like the judge's list than like the nicknames actually on cart, which would also let you justify using things like long nicknames or unicode characters. Now, if you want to say this idea of a third-party neutral judge relaying information is ridiculous, I'll remind you that it was
consistently offered as justification for why HP can be displayed in 100ths rather than strictly out of 48ths and
recently reaffirmed when deciding how to handle Deoxys in the Deoxys Camouflage thread.
The problem with that approach is that, without duplicate nicknames allowed, you end up losing information from Beat Up. Currently, an astute player could identify, based on the damage rolls from Beat Up during a turn, the base Attack of Pokemon in the back, and potentially still gain information on what that unrevealed Pokemon is. For example, if we have 1 2 3 4 5 6, and 3's damage roll was very high, you might be able to calc that and determine there was a Salamence or Metagross as 3, because only a Beat Up roll using 135 attack could have achieved that much damage. Or conversely, you can see that 2's damage roll was absurdly low, only possible with a low base Attack like Blissey. This is going to be most impactful if the damage ranges are initially ambiguous (say it could be possible for the Attack stat Beat Up used for its particular hit to have been anywhere from 125-135), but multiple instances of Beat Up provide additional numbers to narrow the potential range of options. I have no idea if ADV players are in fact doing this in tournament or not, since the damage calc doesn't support Beat Up (and I doubt people are manually adjusting the values in the damage calc to check) but if they were to do so, it'd be optimal. So the distinctiveness of nicknames
matters. But, you can completely circumvent this by not excluding duplicate nicknames! So I think you can do this Beat Up mod, but only if you also
remove the restriction on duplicate nicknames.
Ideally, we'd like it to work like in the latter gens,
here is an example.
We'd probably make it even more straightforward than that, keeping it the same way it is now but changing the text from "<nickname>'s Attack!" to "generic Pokemon's Attack!" or something similar. Beat Up in past gens shouldn't say "it hit x times" (note this is currently bugged on sim) or use the modern Beat Up base power formula. So it'd be more straightforward to just change the text here to remove the nickname, rather than literally use the modern gen implementation.