Why would I want to let a flush draw see 2 cards? They're only calling on the river if they hit...
I didn't mean that it would check all the way to the river and you let them see them for free. I think that 90% of the time, someone is betting this flop. If its a bluff, then they fold to your check raise all in, and you win more than you would otherwise. If its a semi-bluff (flush or straight draw), then they'll probably call your check raise because of the pot odds and they'll get to see two cards.
The key here is getting your opponent to make a mistake. You want them to see to the river with most of their draws here - you just want them to put all their money in on the flop to do that. By going all in you're asking them to call 11370 into a pot of 16170 - a situation most players will avoid here unless they actually have the better hand (set/straight/straight-flush draw). However, if you check, you create a situation where someone can semibluff with say a flush draw, and bet 4000ish into the pot. Now when you check raise all in they're looking at calling 71370 into 20170 pot - a call that they have to make with a hand like AT clubs. They played the hand entirely reasonably, but by checkraising you put them in a situation where they had to call, even though prior to any betting, they wouldn't have been looking to call your all in on the flop.
Now of course, that assumes they're on a semi-bluff with a straight of flush draw - there are obviously a lot of other possibilities.
1) They're on a complete bluff - congratulations, you just won some extra chips that you wouldn't have if you pushed all in.
2) They have a hand -
i) they have a set - you're getting it all in anyway, regardless of whether you bet or check raise
ii) they have a worse two pair - you're getting it all in anyway, regardless of whether you bet or check raise
iii) they have a single pair - if they have top pair, maybe they'll lay it down to your check raise where they would've called the lead-out bet. If they have some other pair, they're probably folding either way, and this way you get the chips from their probe bet
3) no action at all on the flop. I find this scenario very unlikely, since we're at the point where pots with 4 people seeing the flop, even cheaply, are big enough to be worth making a play at. I think most people play pretty aggressively at this stage, especially seeing a lot of weakness in front of them. If there's no action whatsoever, that's probably a pretty good sign that no one has a big enough draw that giving them one card will hurt you.
I think that the vast majority of the time, the check raise gives you a much better chance at making some money off of this hand.