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A "Harrison Bergeron" team would probably be neat.
Naturally the leader would only want to quash the strong and equalize trainer power so only pokemon he controls would be dangerous, etc.
Team uniforms would be unisex, full-body + veil and higher ups would have cool pokemon-themed masks on, as well as weighted jewelry.
One of the earliest "admins" you battle would be revealed to be your booty blasted rival. Maybe even go full edge and have him not learn his lesson after being defeated and return as a post game or sequel boss.
They would be really annoying to fight because all of their pokes have a debuffs of some sort to throw at you, as well as status shenanigans.
Their general grunt incompetence would stem from over handicapping themselves or trying to be too fair. For example, in a double battle, one grunt might burn all your pokes but then his partner will poison all of theirs (some grunts may have Guts pokes).
Can't think of a good team name though. "Team Quash" just sounds silly, although I guess that is the point sometimes.