Not only Shadow Tag, it's because Wobbuffet had the ability to trap almost anything and use Encore. Mind you, Encore lasted for like 8 turns in Generation 3-4 and Wobbuffet had the bulk to survive most unboosted attacks. That means Wobbuffet could do so much for a team - lock an opponent into something like Swords Dance and get a ton of free turns and a forced switch (in case you decide to switch Wobbu out), lock an opponent into a powerful move, trap them, live a hit, then determine which of Counter/Mirror Coat you will use. Wobbufett also got access to Safeguard, so it couldn't even be answered by status, which was an obvious answer to it. If Wobbufett had no chance at surviving another hit, it can just Destiny Bond as to not lose any tempo. The average Wobbu set is Wobbuffet @ Leftovers, 252 HP/64 Def/64 SpD, Counter/Mirror Coat/Encore/Safeguard or Destiny Bond. In short, Wobbufett provided insane utility for a team that could counter nearly everything, leading to its presence in Ubers.
