Either way, if you take a RB #1, you're probably dumb.
If you have the #1 pick, your team sucks. RBs can't produce for themselves (perhaps Barry Sanders excepted). They need an offensive line. If you're so bad that you've got the #1 pick, you probably have a sh!tty o-line. A running back isn't going to help you.
The same is somewhat true of a QB. If you have the #1 pick, you probably don't have the o-line or the offensive skill players to support that QB. That QB--who will be expected to pretty much start immediately--is going to be shell-shocked by midseason. Probably [especially] because he's used to playing on an Alabama or OSU or [insert helmet team here] squad where he's been surrounded by players who have a talent advantage over every single team they face short of the CFP.
Teams keep doing it. Teams keep failing. I'm guessing it's not stupidity. I'm guessing it's pandering to fans who are going to roast a GM if they take a can't-miss LT or edge rusher #1 because their fans look at their sh!tty QB (who is mostly sh!tty because he's got no supporting cast) and want to replace him first with the hottest name on the market even though they don't have the supporting cast for the next guy either.
As a Clevelander I have lots of experience with teams that suck and I've watched the Browns do this repeatedly.
I think that they ruined some potentially great careers because at least some of the QB's they took with high-end picks probably would have had successful NFL careers if they had played for teams with better Olines, WR's, etc.
My position is that if you "earned" the #1 pick or a similarly high pick by being the worst or one of the worst teams in the NFL, I agree with you, your team sucks. At that point you don't need a single superstar at ANY position, what you need is decent NFL level performers at a whole lot of positions.
Separately, I also believe that there is a certain amount of just crapshoot dumb luck involved in NFL selections. You can try to analyze it to death but the reality is that some of those QB's from helmet schools (to use your example) really are great QB's and some just look great because they played on a team where they were, as you put it, "surrounded by players who have a talent advantage over every single team they face short of the CFP".
Combining those two factors, what I think a truly awful NFL team should do is to trade down for extra picks. As a crappy team, a superstar QB (or RB, or even Olineman) isn't going to materially improve things. Furthermore, you simply can't afford for that valuable #1 pick to end up as a bust. If you instead trade for multiple picks from a better team, you get more pretty good guys and you can absorb a bust because you made more selections.
The best value of a really high pick, IMHO, is for a good-but-not-great team that has a specific area of weakness they need to improve. If you are a 10-7 or 11-6 playoff team but not a true SuperBowl contender you might look at your roster and say "Man, if we added a high-end WR to this team, they'd be unstoppable". Maybe instead of WR your specific area of weakness is at DE or RB or LBer or TE or whatever. That 10-7 or 11-6 marginal playoff team can seriously benefit from a properly deployed high-end pick because they can add a superstar to turn that area of weakness into a strength and improve their fringe playoff team into a serious SuperBowl contender.