Healing Strategies (esp. Low Levels)

As both a player and a GM, I've noticed a certain tendency among players that is completely understandable, but also a little misguided...and that is to always heal downed PCs. It's the natural inclination for a PC with healing to want to actually heal a downed PC regardless of the circumstance, but the reality is that there are many situations in which it makes more sense to simply not do that.

A year or so ago, I was playing a warpriest frontliner in Strange Aeons, and when we got to a BBEG and a minion at level 2 or 3, my character was up in her face, doling out melee damage. She knocked him to dying 2 with a crit, and one of the healers (completely understandably) healed him to 10 or so hit points. Well, after being shifted to above the BBEG in initiative, the minion got a solid hit on him, and boom, down again at dying 3. He was healed again, then shifted above the minion in initiative order. When it was the BBEG's turn, boom, another crit, and it was goodbye warpriest. In retrospect, I realized that it might have been a better choice for the healer(s) to simply...let me make death saves. Not sure if anyone had Stabilize, but that would have been a better choice as well, since most (and I do mean most) enemies aren't going to attack an unconscious PC unless the GM is particularly malicious.

Fast forward to some recent sessions I've been GMing, and I've actually seen the exact same thing play out in the exact same way. A frontline melee character goes down, the healer (again completely understandably) heals them, and they get wrecked because they're in the thick of the fray. While it's somewhat incumbent upon the frontline melee characters to try to get out of harm's way, they're at a serious disadvantage when they're prone, often need to grab a weapon, and then leave the square of the enemy. Any reactive strike/shield/similar will proc, and it becomes a dangerous situation.

As counterintuitive as it is, it often makes a lot more sense from a mechanical/gameplay standpoint for healers to just let downed PCs make their death saves. It might not seem or feel right from a roleplay standpoint, and that's completely valid. But in terms of strategy? It's often best to let them have their dirt nap. There are obviously a lot of other "in between" options, and Stabilize arguably exists for exactly that reason. At higher levels, a lot of this becomes a moot point for various reasons (including ease of access to resurrection), but the reason I bring this up here is that I've now seen it quite a few times on both sides of the GM screen, so figured I'd bring it up for discussion.