You push all-in so that you see all 5 cards, and possibly you fold him out (which you don't mind).

This is how T.J. Cloutier recommends how you play a hand which isn't made yet but has a ton of outs after the flop, and it makes perfect sense to me. You semi-bluff at it, and if you get called at least you see all 5 cards. With 14 outs or more after the flop, you are actually the favorite. You're ahead at that point. But if you pay to see just one card and don't make your hand on the turn, you are now the underdog. Even if you DO make your hand on the turn, your opponent may sense this and slow down, not paying you off. I'm not saying you push all-in with every nut flush draw....just if you have other outs besides the flush that make you essentially the favorite or at least almost even money.