I think that's madness, personally.
For starters the logic doesn't make sense. What's more likely to happen? A consensus #1 pick QB to become a very good NFL player or picking up multiple defensive players, many lower in the draft, and all of them becoming good NFL players? Definitely the first.
8 of the last 9 winning Super Bowl QBs were picked in the first 32 picks of the draft. Only Rodgers (24th) and Brees (32nd) were picked outside the top 20. The one winning QB that wasn't, Russell Wilson, was a victim of typical overthinking by NFL scouts because of his size. He'd have definitely gone much earlier if they didn't look too much into silly things.
Even if you look at teams in the playoff hunt this season, the majority are lead by early QBs. Defense obviously helps, but it's an offensive league these days.
The quickest (and cheapest) way to maximise wins is to get a franchise QB.
The simplest way to get a franchise QB is to draft one of the highest rated QB's and give them some playing time in the league and then make a decision on them.
I honestly thought a consequence of the rookie salary cap might be that the awful teams draft multiple QB's in the first few rounds until they find a QB they think can be a franchise QB to build around. There should be no need financially any more to give your rookie QB a 4-year audition before deciding what you've got.
If I was the GM of a terrible team (e.g. Jags, Titans, Raiders) I'd just keep on drafting a QB in the early rounds until I have one I believe in. I wouldn't be pinning myself to one guy regardless of how high I drafted them. It really wouldn't be a disaster to keep cutting players on their rookie contracts if they don't pan out.