This goes for monsters too. But I guess that's off the table.
???
Why is it that "off the table"?
Whether it's efficient for monsters is a different equation though. 99.9% of monsters exist with a 5MWD. They have one combat to shine in, so never need to preserve resources or think about later. On top of that, they usually significantly outnumber the PCs. So you have to work out whether it makes tactical sense for that to heal on that basis.
You can't act as if the same constraints that apply to the PCs apply to them. 5E is in practice an asymmetrical system, but in practice virtually all versions of AD&D/D&D are somewhat asymmetrical so that should be unsurprising.
There's a factor missing from this analysis: misses (and defense in general). Sure, some enemies can deal more damage in a round than the healer can heal, but all that extra damage has to wait until a successful attack. So, it might behoove the poor tank with a healer behind her to use some of those tactics and teamwork that I mentioned earlier to avoid that successful attack.
No, that factor is not missing. If you're choosing to heal when a PC is only lightly damaged, which is what you appear to be describing - healing not when it's necessary but just to "top up" a PC - that's almost certainly a wasteful use of your action. It's a failure of "teamwork and tactics". You know what great teamwork and tactics looks like? It looks a pile of dead monsters.
So yes, I'm assuming the PCs use teamwork and tactics to disable (CC) and kill (HP) the monsters. That's how D&D combat works. If you disagree, please describe the specific mechanisms and actual D&D 5E abilities you're suggesting the "poor tank" should be using to "avoid that successful attack".
1) So does your "focus on killing the enemy," or lack of NPCs doing so, indicate knee-jerk DMing as well?
Why would it? Can you explain? You can't just accuse everyone you disagree with of "knee-jerk DMing". It's a specific critique - and attempting to fix one system without holistically looking at what that impacts is a classic of knee-jerk DMing.
Not every critique applies to every situation. If someone is very forgetful, and you call them a penny-pincher, that's just a nonsense. Equally, you can't just apply "knee-jerk DMing" to every situation.
2) If it's a systemic issue, why are you still playing D&D?
Didn't you ask for civility? I would suggest the hackneyed and ultra-tired cry of "If you criticise D&D at all, you shouldn't be playing it!" to be quite uncivil. A sort of ridiculous gamer equivalent to "If you hate [country of birth of both people involved] so much, why don't you just leave?!?" as a response to any criticism of or desire for improvement in the systems of a country.
And it's particularly bizarre here, because the OP outlined an elegant and efficient house rule that does a good job of addressing the issue. Personally I think every game system has problems, and yoyoing mildly annoys me. But not enough to feel like something needs to be done.