If you think about it, waiting around and letting someone attack you while you do nothing is kind of silly. Undoubtedly, the Pokémon we throw into battle feel that way about turn-based combat too.
Here's a funny video by Shippiddge, where Pokémon decide to stop playing by the rules and just fight normally for experience points. It's not quite as wholesome as regular Pokémon though.
A Wild Encounter [Shippiddge]