I have not seen a sweep or QB draw used in the NFL for years. Why not?
Sweeps are too slow to develop, and are snuffed out by the more mobile linemen today, or by the outside linebackers in a 3-4 defense, yadda, yadda.
They’ve been replaced with the quick out and the swing pass, which is an overhand sweep toss, really.
QB draws are used from time to time. Teams like protecting their QBs, and don’t want to put them in harm much. I’ll leave it to the stat freaks to establish just how often the QB draw occurs.
They’re hard to execute. For sweeps the linebackers are fast and the linemen are slow, it’s really hard to get your blockers out to the edge and make it work. With the sloppy tackling we’ve seen league-wide this year defenses would probably like to have seen some sweeps because they can get better natural angles of attack on the play.
QB draws have a similar flaw. Defenses flow to the ball so quickly. Modern linebackers have been trained to freeze until they see the ball move (this is true of the Steelers at least, I can’t speak for other teams). It’s a lot easier to disguise when it looks like the back is staying there for pass protection.
Well, except for James Harrison, who freezes because he’s held on every play. 
As has been mentioned, the reduction in sweeps is due to the offensive linemen being too slow compared to the defensive front seven. The reason they’re slower than they used to be is that, as the passing game has become more and more important, the linemen have gotten bigger and stronger so as to be better suited to pass blocking, which requires the them to be *relatively *stationary.
Bingo: Big, pass-blocking linemen versus incredibly advanced linebackers (compared to those of yore).
We’re talking about a back running wide after a handoff from the QB, right? I wonder if the trap has seen a similar demise, since it also involves a pulling lineman. On a screen, another play which ostensibly requires mobile linemen, I get the impression anymore that the pass receiver uses the linemen more as “picks” than as blockers.
I miss the trap. The Steelers stopped running it because they got rid of their last real blocking fullback when they let Dan Kreider go. It seems like you need a good FB to run the trap but that might be a familiarity bias on my part. It was never a big yardage play for them but you can pick up some decent chunks of ground with it. I like when a team uses the fullback as a decoy to draw the linebackers over and then runs the HB wide on a stretch play.
Or on a pitchout, yeah, typically with one or more linemen pulling around to block. The sweep was a staple of Lombardi’s offense with the Packers. “What we’re trying to get is a seal here, and a seal here…”
http://www.profootballresearchers.org/Coffin_Corner/19-05-712.pdf
Not sure if it’s a technical ‘sweep’, but last weekend the Cowboys faked this pitch as a run and froze the blitzing end.
Jones’ 49 yd TD
I haven’t seen Romo QB draw without there being some kind of breakdown (and the play is going on for more than 5 seconds)
I think Vince Young has run a QB draw in the NFL, and possibly Michael Vick.
Ben Roethlisberger has run them but not recently. The most salient ones for me were in the AFC championship game in his rookie season against New England. NE stopped blitzing and dropped everyone into odd coverages to confuse Ben and it worked. Ken Whisenhunt resorted to putting Verron Haynes in at RB to lead the draw for Roethlisberger since they had a numbers advantage in the middle of the line now. He wasn’t trying to get big yards but to force NE back into their base defense. Bill Belichek won the battle; I don’t like the guy but he did a lot of things right in that game.
I don’t recall many others being run since then by the Steelers but the Jags run one against them in the playoffs and it won them the game. Plug your ears non-Steeler fans because that was the beginning of the complaints about some nameless LB being held all the time. The league did acknowledge the hold too but as Rod Woodson always says, you have to outplay the officiating and Pittsburgh didn’t that day. the QB draw was the back-breaker.