In reference to the TJ, the basic thinking is that <x> years after having it which i believe is 5 is the time where if you are going to have issues the issues occur. Obviously that's not exactly a sure fire reason to avoid someone because presumably if you're signing him the physical will check that. Just saying it's a concern some have.
As for the rest of your points, again to me it comes down to price. I think Zimmermann while probably slightly better than shark is likely to get over paid relative to his value. Incidentally, your comments about ground balls is apt to Shark because a lot of the reason he was successful in 2014 is he pitched to ground ball contact in the early innings and used his stuff later in the game to strike people out. To me it's just a case that Shark is a good and probably not great pitcher. At $15 mil/season I can live with that especially if he has the talent to pitch like a #2 at times. The problem with Garza and Jackson is they were probably #3's and forced to pitch as #1/2's as there was no one ahead of them.
With Zimmermann, from the rumors, it sounds like $20 mil/season is his floor in which case I honestly think he's going to be over paid. Excluding 2014 over the past 5 years he's been worth an average of 3.35 fWAR. That roughly puts a fair value on him around $21 mil/season using $7 mil/WAR. If he starts to creep in to the $22-25 mil/season range he's slightly over paid. With Shark, if we exclude his 2014 to be fair, he's been worth 2.7 fWAR the past 4 years he's started. That using $7 mil/WAR makes him roughly a $19 mil/season pitcher. If you get him at $15 mil/season that's value.
As I said, my numbers could be wrong for what these players are looking at. I'm just going off what's been reported and while they do have sources half the time they are wrong. If Shark is more expensive than he presently appears to be then Zimmermann probably makes more sense. However, as I said before, I don't think roughly half a fWAR difference between the two is worth a $5 mil/season difference. Also, if Zimmermann is in the $22-25 mil range he's probably realistically looking at 5-6 years where as Shark's probably looking at 4. That makes a difference. It's not just a case of "who's the better pitcher?" It's about how the players value plays for the team. If Shark is $5 mil cheaper that could be the difference between signing someone like Span and signing someone like Heyward to play CF. Some don't like the idea of Heyward and that's fine but the point still stands. $5 mil can make a large difference in the caliber of player you get else where. Also, even if you don't spend that money, as I suggested before, you might be able to front load some of Shark's deal in such a away that he's say a $10 mil player the final 3 years which frees money for re-signing young hitters or doing something in FA down the line.