But why do you feel that you *have* to have them do that? Why not just accept that having PCs bounce back up quickly is part of the game and roll with it?
Good question. It's not just because bouncing back ISN'T part of the game unless the DM holds back on using the rules (whether because she's a soft carebear or simply doesn't see how easy it is to double-tap fallen heroes).
I feel quickly bouncing back is a cheesy notion, or more specifically: how whack-a-mole strategy is pure cheese.
Furthermore, I don't like the vindictive turn the game takes if you take the rules to their logical conclusion; i.e. double-tapping. I don't want a game where you actively want to kill the heroes just because the rules don't make them stay down one bit. It only justifies the player characters into becoming even more murderhobo (if they actively try to kill us, then we have no qualms with killing them)
How is it adding "insult to injury"? It's a system that works well enough in other games, like the aforementioned Dragon Age. It's even one of the suggested options in the DMG for using the lingering injuries mechanic. I think it makes more sense that being "taken out" in physical combat would result in a lingering wound of some kind than some of the other ideas being bandied about in this thread do.
D&D isn't those other games.
I believe that you will get downed on a semi-regular basis, and since there's usually very little you can do about it, I refuse to penalize this even further.
More generally: lingering injuries is solving a different problem.
Your problem is "being downed does not carry enough of a consequence". That is a fine problem to tackle, but I'm not the one having it.
My problem is "better to hold off healing until he's going down, since we then get rid of some damage". My problem is whack-a-mole. Nothing about lingering injuries make you want to stop healing the fallen. Nothing about penalizing the PC that takes damage chnges the fact that surplus damage disappears at 0 hp.
Then instead of mucking about with adding negative hit points and the like, why not just make it so healing word can't be used on someone who is dying? You could make it so the target of healing word has to be able to hear you as well as you being able to see them, and if they're dying, then you could say that they're effectively deafened and therefore can't hear you. That way healing word would only work on someone who is "still standing".
First off, there's nothing complicated or "mucking about" with negative hit points. In my opinion, it is a very easy and straight-forward mechanism.
Secondly, I don't want to create exceptions for specific spells. That, if anything, would be "mucking about" in my world. Why would a d4 healing word not work when a 1 hp Lay on Hand does? Why would a Healing Potion work even when you roll a one, when a healing word won't work even for a Life Cleric using a level nine slot restoring dozens and dozens of hit points? (And so on, I'm being rhetoric)
Drawing the line at -10 instead of 0 treats all healing equally, which is a trait I happen to appreciate.
But good luck with your campaign and your lingering wounds!