I really like the entire idea...and I'll happily spend £3.49 a year for it.
Last week, I was at the Pokémon Adventure Tour here in Bournemouth, battling the experts and various people there once they realised who I was. However, I suddenly wanted to change my team...but oh no! My Durant is on my Black, while I only have Black 2 on me. I guess I can't use that team.
Skip forwards to a hypothetical year. Same situation. I'm there with X, but I need to use a Pokémon I captured in Y. Luckily, I put all my Pokémon into my Pokémon Bank for easy access. I connect my 3DS to my phone, grab them from the box, and battle.