That’s what the original Sym on launch did, (probably why it’s like that in HotS in the first place) and it didn’t work. Her original E ability was a buff that gave an ally 50 shields until they died. It got nerfed to a worthless 25 shields within about two weeks because it made divers and a few other characters too much of a menace. That’s why they made it an ultimate with an application range.
They tried out a lot of stuff behind the scenes before Syms first rework and tried a lot of stuff before this one. A lot of the stuff the devs name dropped as having tried were suggestions the players proposed. And honestly, I’m not surprised that even the good suggestions didn’t work, because even if the suggestion solved one problem, Sym still had several others.
For example, making turrets heal, give shields, or give other effects wouldn’t change the fact that turrets themselves are easy to destroy, even with 15 or 30 or whatever health. That puts Sym on par with Ana for unreliable support if it made it through. Sym’s ults are still just ok, and even all the QoL stuff added doesn’t elevate them to great. I’d still rather have Moira or Mercy ult than Sym ulting because those can save you from death. That’s not touching the aforementioned Schrodingers weapon, which has so many problems yet takes up so much kit power.