Yea he's a strange one, I think most people realize that his production is mostly just a function of the threat of our other offensive weapons but if you look at the contracts given out to Hunter Henry and Jonnu Smith by the Pats last year (12.5/year) and their statistical production, there's a strong argument that Schultz's floor is that yearly average.
But on the other hand it's pretty obvious that he's nowhere near as dynamic as guys like Kittle, Andrews and Kelce who are only making like 14/year, or even Goedert who is making just north of 14/year, but Schultz's statistical production is close enough to Goedert's that I'm sure his agent will push for that salary range.
For me, I wouldn't go any higher than about 10, maybe 11/year on him, but once you start talking 12-14/year I think it's just too much. You're paying him like a top 4-5 TE in the league at that point and I don't think that's what he is, nor is it good value on a roster where we have to be judicious with who we're paying now that Dak is on a big deal.
There's also a bunch of other FA options at TE who I think could come in and give similar production for probably half the price with guys like Evan Engram, Tyler Conklin, Gerald Everett, OJ Howard, and Maxx Williams. There's some injury risk with a few of those guys but I'd much rather roll the dice on them at 5/year than Schultz at 13/year. I also personally think Gesicki is a better TE than Schultz, so there's an outside chance that he tops the market and then Schultz is kind of left with the leftovers and we're able to get him back for a bit under market value.
This is also a strong TE class in the draft in the 2-4 range, there aren't any Pitts or Hockensons in the first but there are a number of guys who we could get in that 2-4 range who I think could pretty comfortably replace Schultz by their 2nd season.
The other complicating factor is the Gallup situation. By most measures we can only afford to keep one, and Gallup is pretty clearly the more talented player but his market may be depressed given that his stats are down with the injury. If the choice is Gallup at 10/year or Schultz at 13, I'll be taking Gallup.