Against 1 or 2 villains, sure I c-bet, but against 3 villains in this spot, I gladly just take the draw and let the flop check through.
Odds are good that if we bink on turn we can get super juicy value out of a ton of TPGK or two pair combos and if we are really lucky we can prison rape a slow played set
Another reason I like letting the flop check through is because if we miss on the turn, we give ourselves great implied odds to call most turn bets.
In general, I like c-bets when we can retain the initiative, take down a decent sized pot, and have an okay board texture (and image) in which we should have fold equity. Against 1 or 2 villains I'm c-betting like 90% of the time. But against 3 villains, I cut my c-betting percentage down to like 40%. Another factor that impacts my c-betting is whether or not I'm drawing to the potential nuts in a situation where if I hit, I can get super juicy value from lessor hands that will feel compelled to call however if I c-bet, I may push out those potential hands...
So with all that said, I like letting this flop check through more than I like c-betting it. The tipping point for me is 3 villains instead of 2 villains or less.