I look at it a different way...
If you have the #2 pick in the draft, you have a sh!tty football team. That's how you got the #2 pick.
Now, for some teams it's a down year in a good organization. For other teams (I'm looking at you, Cleveland) it's a consistently terrible management structure that produces perennially bad teams.
So if you've got the #2 pick and you're a bad football team with bad management, what are the odds that you're going to ruin your draft pick? Probably higher than one would think...
I'll bet if you look at #30-32 picks you'll see a lot of successes. Because they're being drafted by competent management in successful organizations and given every opportunity to succeed.
I like this as a novel theory. But I see a couple issues.
1. A lot of those bad ones didn't even get fourth-year (or is it fifth-year?) options picked up. Basically, a lot of these teams ruined guys so badly, they didn't even want to deal with a sunk cost.
2. If that was the case, I'd imagine we'd see some reclamation projects. And in truth, we usually don't.
I like the 30-32 idea, and I found a site that tracks such things. From the same span of years, 2001-2017 here's each:
30: T.J. Watt, Vernon Butler, Damarious Randall, Jimmie Ward, Alec Ogletree, A.J. Jenkins, Muhammad Wilkerson, Jahvid Best, Kenny Britt,Dustin Keller, Craig Davis, Joseph Addai, Heath Miller, Kevin Jones, Sammy Davis, Kendall Simmons, Reggie Wayne
31: Reuben Foster, Germain Ifedi, Stephone Anthony, Travis Frederick, Doug Martin, Cam Hayward, Jerry Hughes, Beanie Wells, Kenny Phillips, Greg Olson, Kelly Jennings, Mike Patterson, Rashaun Woods, Nnamdi Asomugha, Robert Thomas, Todd Heap
32: Ryan Ramczyk, Malcom Brown, Teddy Bridgewater, Matt Elam, Derek Sherrod, Patrick Robinson, Ziggy Hood, Anthony Gonzalez, Mathias Kiwanuka, Logan Mankins, Ben Watson, Tyler Brayton, Patrick Ramsey (only 16 of those as first rounders)
At 30, you have Wayne, Watt, Miller, Wilkerson I guess. So you're still at like 60 percent of
Joseph Addai, Dustin Keller or worse.
At 31, Hayward, Fredrick, Olson, Heap were good. I have no good read on Asomugha. Hughes was decent, same with Jennings, Patterson
At 32, In the good category, Ramczyk, Mankins, kinda Ben Watson Solid: Brown, Patrick Robinson, kinda Bridgewater. So a QB who was healthy for two years make the top half with ease.
Basically, no matter where you take someone, there's a better than half chance they bust and a 80 percent chance they at least disappoint your expectations.