My only fear is that it's too late in his evolution to do it. It's comparatively easy to get a QB to throw it away in order to protect himself. He did that in 2023. I imagine it's much harder to ask someone to start running when doing that is by definition an instinctive action.
To my eyes, Tua used to play a lot more recklessly. For instance, watch the 2018 highlights and note how much he's always moving. He also ran around in the pocket a lot more making him look like a Russell Wilson type.
2018 Highlights featuring an ever-moving Tua:
Every year since though, he's seemed to become a bit less mobile and a bit more stationary in the pocket (which probably helps accuracy). But he's less inclined to move instinctively like he used to when he first emerged on the national scene.
I wonder if there's still time left to try and find the perfect balance. We've seen a few jukes. Like you, I just wish he'd lose the weight. I don't see that really doing anything to "keep him healthy." More padding around the mid-section ain't keeping you on the field IMHO.
A lot of people probably don't want to admit it, but the best shape Tua was ever in was probably 2020 when he showed up. Yeah, there was some flexibility rehab I'm sure continued on and a bit of improvement in shear velocity with the arm in 2021 but in terms of mobility he was as good in 2020 as he's ever been since then.
A short Flores-era compilation of Tua running: