All depends on when they're called. Averaging 5 or 6 yards on screens on 1st an 10 is a lot different than averaging in on 3rd and long. I look at a lot of the screens as running plays and I would say their yards per play has been equal or higher than our yards per rush attempt. Sure some are going to stopped for a 2 or 3 yard gain and some are going to tackled for a loss, but just like running plays they slow down the opposing pass rush and are fairly safe calls. Sure I would like them to be more effective, but I think the offense has much bigger issues than the screen game.
I don't think that screens have the same amount of value as running plays. A screen is blocked differently, and attacks a different part of the defense/is defended differently. I honestly believe that a 3 yard power run is a far more valuable play to pile up over the course of a game than a 3 yard screen pass.
I'm not talking about the three yards and a cloud of dust offense here, incidentally. I hate that stuff, too. But we saw our offense last season have some pretty fun and exciting games when we followed that formula of Ajayi + deep passing and managed to execute it well. I would hope that we can get back to that.
Now, I agree with you that screens are something that can slow the opposing pass rush, but there are other ways to slow the pass rush. I understand that Cutler and the team might not be capable of running the hurry up right now, but as others have said many times (hi, hoops!) tempo has proved time and again to be a way to slow down the pass rush. We've seen this especially in the performance of our Dolphins in the 2 minute drill in recent years.
I think that if we cut back on the number of screen pass plays we call (currently about 7-8% of our called plays), and replace those with runs, we would see better results over the course of the game.
Incidentally, this is one reason why we needed to invest in another running back. I like Damien Williams as a receiving threat, but I don't think he is the real solution as a guy to spell Jay Ajayi.