I like this idea. I've thought of it myself before. The way I'd like to see it implemented is like this:
Whenever you want to go on elements trainer, you need to type a nickname. Anything you want that isn't used by someone already on the trainer. It does not have to be in any way connected to the official elements. PvP and PvP2 should be removed as it already is, but the "PvP Duel" button would still be in trainer. If you clicked it in trainer, you would be able to type the nickname of the person you want to face (say a friend, to test the deck against or just to have fun, considering you would need to know their nickname) and then battle with no consequences to any accounts or anything. Another option would be to have a "Random PvP Duel" and duel a random person also on the trainer (keep in mind this does not connect with your real elements account in any way, I just thought this might be a pretty fun way to test decks against other specific decks or the like)