I might say that having 3 first picks out of 12 years is pretty much stinking up the NFL.
Every team has bad stretches. In the mid-70s the Cowboys picked 1-1 (1974), 1-2 (1975), and 1-2 (1976). Then they had another stretch where they picked at 1-1 in 1989 and 1991. I won't say who they got with those picks because it'll just piss you off (think triplets).
Imo, just because you didn't have the #1 pick, doesn't mean that you didn't suck. So I like to look at a range. We could say top 5 pick, top 10, or top 15 to define the teams that suck. Here, I used top 5 going back to 2002. The Houston Texans have had a top 5 pick in 4 of those drafts. Three of them in their first five years, which should be expected since two of them were in their first two years as an NFL franchise.
Detroit 6
Washington 5
Houston 4
Kansas City 4
Oakland 4
St Louis 4
Arizona 3
Buffalo 3
Cincinnati 3
Cleveland 3
Jacksonville 3
Miami 3
Tampa 3
NYJets 2
San Diego 2
Atlanta 1
Carolina 1
Carolina 1
Chicago 1
Dallas 1
Denver 1
Green Bay 1
Indianapolis 1
Minnesota 1
New Orleans 1
NYGiants 1
NYJets 1
Philadelphia 1
San Fran 1
Seattle 1
Tennessee 1
The Texans are now going into their 14th draft. In the last six (going back to 2009) we've only had one top 5 pick. In fact, we didn't have a top 10 pick other than 2014. In four of the last five years, we haven't had a top 15 pick.
That's progress imo.