I think it had to do with (a) his contract, wanting to get a new deal instead of those one year incentive-laden deals, and (b) long-term tensions with the Patriots medical staff over rehabbing and returning too soon.
This counts for zero on a message board, but I have a family member who knows Gronkowski's father (he's in the gym/fitness equipment business.) These are the two things he griped about; I can't be sure Rob shared the same viewpoint, but clearly he had issues. And to your point, I think the burning out part may have to do with the fitness regiment/conditioning program and back to suspected injury causes. I'm sure Alex Guerrero and Brady's take on the workouts/long-term health stuff just added fuel to the fire.
I understand the team's perspective and the player's perspective. And I wish Brady/Gronk had a more trusted authority than Guerrero because I think there is a lot of validity to what they wanted to do in terms of load management.
But yes, anyone who says Gronk was a diva is totally warped. Gronk is one of the most unselfish superstars you'll find in sports. Just a genuinely nice person who never let fame and money get to his head. Never hesitated to be a decoy, or a blocker, or whatever gave the team the best chance to win.