Unique Pokémon should not be playable.

From the very beginning I've had my reservations about players being able to capture and fight with unique Pokémon. I absolutely loved using Mewto in Pokémon Red but I could never really let go of the realization that I was using a Pokémon that was fundamentally overpowered, and was made so by design. To confound the problem, many unique Pokémon--i.e. Pokémon of which you can only obtain one during regular play--are Legendary Pokémon, Pokémon that fulfill important cosmic duties and sometimes literally contribute to keeping the Pokémon universe in balance. But in-game? You can fight them, wear them down and catch them like any other Pokémon. I know that hordes of people have made this observation, but I don't see anyone clamoring to rectify this weird situation where you can challenge the Elite Four while wielding the literal God of the Pokémon world. It just erodes the status of these god-like Pokémon when you can just use them as normal, and it becomes even more incredulous when 'regular' Pokémon turn out to be more powerful than they are! 

The weirdness continues in WiFi battles where players can face off against one another both using the same unique Pokémon, shattering any suspension of disbelief: the unique Pokémon becomes just another bundle of stats and is divorced of any meaning as it is just another tool in the arsenal; just one that is slightly harder to acquire.

Players should not be able to fight with unique Pokémon such as Arceus, or Victini, or Mewtwo. They should be part of the world, and referred to by its inhabitants--maybe you can even see these magnificent, legendary Pokémon if you are lucky--but you should not be able to fight them, let alone catch them to help you stomp out the next horde of Zubat you encounter in a cave somewhere.

Pokémon should encourage players to play with the Pokémon they like, this means that every Pokémon should be usable in-game. Because of their very identity as unique Pokémon almost all of them are patently more powerful, blessed with higher stats and unique and very powerful moves. In the popular Smogon system many of these unique Pokémon are actually confined to their own separate tier so they don't mix in combat with most of the other non-unique Pokémon because they're way too powerful! 

And they're absolutely right. Mere mortals should not compete with gods in Pokémon games.