Garoppolo might be the only QB that I would have any significant injury concerns with. And I don't think he's a franchise guy anyways, so I'd have other reasons for not wanting to commit to him.
Tua's concussion concerns are grave just because of the potential for a next one to be a career-ender.
Prescott's had injuries in two of the past three years, one major, but I don't think he's particularly likely to have another.
Stafford's coming off an injury and had another big one earlier in his career. Maybe there is concern with his age but not really.
Allen's banged up his throwing arm a few times, he doesn't usually miss games because of it but it impacts his play. Not particularly concerned moving forward, at some point he may need UCL surgery and miss a year but he should bounce back after that even if he loses a bit of zip or precision.
Watson and Burrow have both torn ACLs. They've seemingly recovered fully, so no forward-looking concern. Brady had the same injury a long time ago, missed a year then was fine.
Rodgers broke his collarbone in both 2013 and 2017 (not sure if same one), that can be somethng that recurs once it goes the first time, but he's been fine since.
Luck had two major injuries in his 20s. Not sure how much of a factor those were in his retirement.