JwThis is why it's important to appeal to competitive-minded people to begin with, rather than just TF2 people in general. Purebred casual players simply play a different game than us. Maybe trying to get people who already play competitive movement FPS games to test out 6v6 TF2, or having some kind of ELO-based matchmaking service that only appeals to competitive-minded players in the first place would work.
Even if we accept that the gap between 6s and casual is large, the solution can't be to just throw up our hands and give up on attracting TF2 players, because the gap between 6s and another game is even larger. Sure, players from other competitive games might have a better mindset and have better aim, but TF2 has tough mechanical and knowledge curves just like any other game. The success rate of recruiting them will be low because unless they really like the experience from the outset and want to make it their primary game, the potential hundreds of hours they could put into getting halfway decent at TF2 by competitive standards could be put into getting even better at whatever game they came from. Teaching casual TF2 players 6s is not teaching them how to play a whole new game, but teaching them a new way to think about their favorite game that they already know the mechanics of and enjoy playing.