Let's try to focus the discussion on the combination of Swagger and Prankster (and possibly Foul Play). While Thunder Wave is usually part of the strategy, possibly making it even more uncompetitive and annoying to face, it's not the main problem here. There are ways to play around paralysis that don't revolve around the use of gimmick/obscure Pokémon. Ground and Electric types are common enough to make Thunder Wave a manageable move.
I think the consensus is that Chansey is a full stop to the SwagPlay strategy. I'd like to ask those who use Chansey, how viable it is on non-stall teams. I've personally never used it (HO player here).
Swagger + Prankster is only problematic when combined with the other parts of Swag Play, which are Thunder Wave, Foul Play, and Substitute. Each of these things on their own are fine and have fair, relevant uses.
The problems, in my opinion, are caused by foul play. The reason I believe this is the case is that it allows defensive pokemon, like Klefki, to fully invest in being as tanky as possible, while also giving it the ability to deal huge damage to certain opponents. Ideally, a team would be built to win, right? So we can agree that, aside from full stall teams, a team would include powerful pokemon that can deal quite a bit of damage, and are invested in their attack stats. Teams counter these powerful pokemon by using defensive pokemon. We'll use Klefki again for this example, which has the best defensive combination in the game. Klefki can be used to wall certain threats, and has a cool use as a utility pokemon, being able to spread status, lay down spikes, and dual screens. It does it's role well, but very few people actually use Klefki in this way. More often than not, people are using it in the form of Swag Play. When this happens, Klefki is able to step out of it's intended role and perform the job of not only an excellent utility pokemon, and can often times become a full-sweeper, who is bulky by nature. It is allowed to be lethal without actually investing any EVs into attack stats, and is allowed to be fast without any investment into it's speed stat through the use of paralysis' side effect of reduced speed. Klefki, when used in this way, is also allowed a significant chance at the removal of autonomy of the opposing player. Due to Prankster, it is also not able to be reliably revenge-killed, and instead, is able to use Swagger on the incoming revenge-killer, thus turning the game into a very important coinflip, which can often determine the result of the game. This is, by nature, uncompetitive.
The set, as a whole, must go. However, each of it's parts has a fair use, and the pokemon who abuse this strategy have other great uses and do not deserve to be removed from the game. Swagger + Foul Play on Prankster pokemon, then, is unfair, and should not be allowed for use. This option removes the strategy, while also not touching anything not deserving of a ban.
