You can do this already in daily chess. Just play that if it's such a big deal to you.
This is a huge issue in daily chess tournaments as well. Both live and daily tournaments attract cheaters for who knows what reasons (the "prestige" of winning a newbie tournament?).
So simply resigning against new accounts is not a solution. Also, even if they do get caught cheating and banned while the tournament is ongoing you get the rating back but you still have the loss in the tournament standings.
So I guess the answer is not to play bullet, not to play tournaments, and just let the smurfs have their fun and hope the regular players won't notice and/or get annoyed enough to unsub from this website?
bump