This may be incredibly naive but being QB is the most critical position probably in all team sports. Why would a later-mid (4th-6th round) be used to pick one if they are not expected to compete to be a starter? Seems to me we wasted picks on QBs recently. There will always be free agent QBs available as back ups.
A few of these are third rounders, but I think the point remains, and sure, you might roll your eyes at a few of these guys but there are also Hall of Famers in this group.
Joe Montana drafted 3rd round 82nd overall
Dak Prescott 4th round 135
Russell Wilson drafted 3rd round #75
Kirk Cousins drafted 4th round #102
Matt Cassel drafted 7th round #230
Ryan Fitpatrick drafted 7th round #250
Matt Schaub drafted 3rd round #90 (don't laugh, 14 year career, 2 Pro Bowls, and has taken a team to the playoffs, went 12-4)
Matt Hasselbeck 6th round #187
Mark Brunell 5th round #118
Elvis Grbac 8th round 219
Trent Green 8th round #222
Brad Johnson 9th round #227
Rich Gannon 4th round #98
Don Majkowski 10th round #255
Mark Rypien 6th round #146
Doug Flutie 11th round #285
Steve DeBerg 10th round #275 (not to be confused with Chris De Burgh, singer of 80's love ballad "Lady in Red"
Dan Fouts 3rd round #64
Joe Theismann 4th round #99
Ken Anderson 3rd round #67
Roger Staubach 10th round!!!!!
And of course the GOAT, Tom Brady 6th round #202
Nothing wrong with taking a guy in the middle rounds, you don't know the future. A quality back-up QB is an important position in the NFL. Taking a guy in the 4th round doesn't preclude you from drafting a QB in the 1st round next year, and who knows, you may end up with two franchise QBs on your roster, which is a good problem to have.
Drafting isn't plug and play, black and white. There's usually a significant development curve and growth that needs to take place in order for a 22 year kid to be a productive pro in the NFL.
I remember reading that Nassib did exactly what the Giants expected from him. Just like David Carr, he never really played a meaningful snap, but was much less of a cap hit.