Greenstein isn't the only one that folds

[Arnfinn Madsen]

I read the post about a line that resulted in Greenstein folding. I have been paying attention to it since and have noticed that quite a few other players fold as well. It goes as this:

You openraise from CO/button and only the BB calls. You hit a relatively non-drawy flop well and BB checkraises you on the flop. You call and then raise him on the turn. I think some opponents fold too often then (can be used as a bluff line, but that is not the point here) and thus against relatively many opponents it is better to postpone the raise to the river (given you are still not too afraid of free cards of course), since they seem to call your river raise (looks more shady I guess). Thoughts?