They also do it when they have a starter who hasn't lived up entirely to the promises of becoming an elite QB. Such teams, if they are competently run, invest in a high ceiling QB if given the opportunity... Consider the Chargers who had Drew Brees as a starter investing in Philip Rivers. Consider the 49ers who drafted Colin Kapernick after their former top pick Alex Smith didn't live up to expectations... Consider Kansas City who drafted Mahomes even with Alex Smith pencilled in as their starter...
Tannehill has been mostly good since he was drafted, but never elite. I believe he could become a Top 10 QB, but that is far from guaranteed. More likely he will remain a middle of the pack QB, which isn't good enough. Another interesting thing about the aforementioned teams is that once they invested a high pick in a QB, the middling QBs had career years... Brees and Alex Smith had their best years with those organizations after being pushed by a highly picked rookie QB. Perhaps it would have the same effect for Tannehill.
There have been 49 QBs drafted in the first round since 2000. Exactly ZERO teams drafted a QB in the first round as an insurance policy. They all fell into one of three categories:
1. No legit QB on the roster
2. Legit QB with 11 or more years of experience
3. Had a starter that was dramatically under performing (Brees) or was thought to be washed up (Warner, he had started 7, 2, 10, and 10 games over the 4 seasons prior to drafting Leinart)
At the time that the Chargers drafted Eli Manning, Brees had thrown more INTs than TDs, despite having the best RB in the league. In 2003, Brees was out performed by Doug Flutie. He was DONE in San Diego. That is when teams draft QBs. Tannehill has been miles and miles better than Brees during Brees' first two years as a starter.
In the end, the only example you can come up with was a mistake by the team that drafted the QB in the first round.
Here is the complete list:
Year Pick Name Team Current QB Exp
2017 2 Mitchell Trubisky Bears Cutler, Hoyer, Barkley
2017 10 Patrick Mahomes Chiefs Smith 11
2017 12 Deshaun Watson Texans Osweiler
2016 1 Jared Goff Rams Keenum, Foles
2016 2 Carson Wentz Eagles Bradford, Sanchez
2016 26 Paxton Lynch Broncos Osweiler
2015 1 Jameis Winston Buccaneers Glennon, McCown
2015 2 Marcus Mariota Titans Locker, Whitehurst, Mettenberger
2014 3 Blake Bortles Jaguars Henne
2014 22 Johnny Manziel Browns Weeden, Campbell
2014 32 Teddy Bridgewater Vikings Cassel, Ponder
2013 16 EJ Manuel Bills Fitzpatrick
2012 1 Andrew Luck Colts Orlovsky, Painter
2012 2 Robert Griffin III Redskins Grossman, Beck
2012 8 Ryan Tannehill Dolphins Henne, Moore
2012 22 Brandon Weeden Browns McCoy, Wallace
2011 1 Cam Newton Panthers Clausen, Moore
2011 8 Jake Locker Titans Young, Collins
2011 10 Blaine Gabbert Jaguars Garrard
2011 12 Christian Ponder Vikings Favre 20
2010 1 Sam Bradford Rams Bulger, Boller
2010 25 Tim Tebow Broncos Orton
2009 1 Matthew Stafford Lions Orlovsky, Kitna, Culpepper
2009 5 Mark Sanchez Jets Favre 18
2009 17 Josh Freeman Buccaneers Garcia, Griese
2008 3 Matt Ryan Falcons Redman, Harrington
2008 18 Joe Flacco Ravens Boller, McNair
2007 1 JaMarcus Russell Raiders Aaron Brooks, Andrew Walter
2007 22 Brady Quinn Browns Frye, Anderson
2006 3 Vince Young Titans McNair 11
2006 10 Matt Leinart Cardinals Warner, McCown
2006 11 Jay Cutler Broncos Plummer
2005 1 Alex Smith 49ers Rattay, Dorsey
2005 24 Aaron Rodgers Packers Favre 14
2005 25 Jason Campbell Redskins Ramsey, Brunell
2004 1 Eli Manning Chargers Brees, Flutie
2004 4 Philip Rivers Giants Collins
2004 11 Ben Roethlisberger Steelers Maddox
2004 22 J.P. Losman Bills Bledsoe 11
2003 1 Carson Palmer Bengals Kitna
2003 7 Byron Leftwich Jaguars Brunell
2003 19 Kyle Boller Ravens Blake, Redman
2003 22 Rex Grossman Bears Chandler, Miller
2002 1 David Carr Texans N/A
2002 3 Joey Harrington Lions Batch, McMahon, Detmer
2002 32 Patrick Ramsey Redskins Banks
2001 1 Michael Vick Falcons Chandler, Kanell
2000 18 Chad Pennington Jets Lucas, Mirer
One other thing to mention, the majority of QBs on the list failed as NFL QBs and would be a downgrade from Tannehill.