1.) Most PvP tournaments and events have deckbuilding restrictions (this is so that decks like poison dials aren't allowed, or aren't nearly as strong). In my Sacrifice event, for example, only one player even has access to Sundial. Furthermore, cards like Dimensional Shield and Discord are banned, while rainbow decks are impossible to build. But I don't see you on the sign-up list...
2.) Furthermore, a lot of the best PvP decks are unthinkable in PvE. This is for two major reasons. The first being that the opponents are simply different. PvE opponents usually have more than 100 health and most of them have double draw. The second is that PvE is about farming as much gold as possible, as opposed to having the highest win rate possible. As a result, deckouts and OTKs are not nearly as good for PvE as they are for PvP.
I also agree with the points made by theelkspeaks.
And lastly, as I've said before, there's not a perfect 100% correlation between trophies and PvP ability. Yes, there are some players who have fewer trophies who are stronger than players who have more trophies. I remember dragonsdemesne had a lot of 2nd place finishes before his first tournament win, and now he's one of the very best players. So, yes, it's possible that you could be a good PvP player and not have any trophies. I never said it wasn't. The reason I want a minimum PvP requirement is that it's not worth risking an inadequate mentor. It's not worth the chance that some of our Mentors could be just as inexperienced in PvP as their apprentices.
I met a guest a few days ago who had been playing Elements for only two days. His mono fire deck, while far from being perfect, was probably stronger than some of the decks I've seen used by players who have been here for months.
We have so many people who are willing to be a Mentor. We only need half of them, at most. So, why take the chance that some of our Mentors could be inadequately experienced in PvP? We want our apprentices to have top quality Mentors, and nothing lesser.
Ah, well. I can only hope that they'll choose players like Odii, Spike, and Blacksmith.