The TTK in this game is decently high compared to other games, this could technically increase it by a bit as well, and also throw off some timing.
Honestly, there isn't really anything wrong with the healing system IMO, it might be a tad boring not being able to do much when healing, but if it's in a good spot, why try to improve it?
The issue you're describing is that healing takes too long, but if auto healing were to be implemented, it should take the same amount of time, or slower, compared to normal healing, as you'd otherwise be throwing the healing balance upside down.
Players need to make decisions, and time these well enough, if they don't, they get punished.
So if they decide to engage with little room for themselves to get themselves up and running again with heals, that should be punished if they can't hold their ground against their enemy.
Fights will likely drag on for longer with this as well, which could have the opposite effect, resulting in longer fights and slower paced gameplay.