Ath-kethin
Elder Thing
Again, like the older editions, no one recovered from near death in a day's rest, so using the Slow Healing DMG variant, helped to simulate that. Also with a cleric with the healer feat in the party, made regaining hit points has proved to be an easy task. It also put more emphasis of having a cleric in the party, as I found in other games (like Pathfinder and a multiple wands of cure light wounds) to make out of combat healing trivial. This puts a little more sting in getting injured and worn down over time (without a cleric in the party) and helps put fighters and barbarians, or other melee types in check (as I found optimized melee types to be very very powerful in my groups I've run, overshadowing spellcasters or other types).
Again this was designed and used to make it 'feel' a bit more like the older editions (1e and 2e), and more realistic for being badly injured - - it takes longer than a day (naturally) to be back to full fighting health.
Thoughts?
YIDM
I understand why you want to implement the slower healing. As I mentioned, I am a 2e veteran myself; the gonzo healing was a big chunk of why I passed on 4e, and I had originally planned to slow healing down in my 5e games as well.
But I am mainly a DM, not a player. What I found as a player was that the standard 5e healing speed meant one less thing I had to keep track of and worry about. As a DM, it means as many less things I need to keep track of as I have players. And it helps facilitate the kinds of stories I like to be involved with, specifically sword-and-sorcery type stuff like Conan and Fafhrd + Grey Mouser. None of whom spent time holed up in a hospital room or wearing a cast on their leg slowly recovering from injuries.
Now, I also don't allow any full casters except warlocks in my campaigns, so there's that. But mostly, I'm curious as to whether your players were interested in an exponentially more challenging game, with far more accounting involved.
One thing I love about 5th edition is how nobody agrees on which classes are "overpowered." The fact that you can make a case for the melee types to be too strong says a lot about the quality of the overall design. And it's your game; there's no wrong way to play it. Do what works for your table. I've just never seen a group of players who were as interested in going back to the "bad old days" of weeks-long recovery from combat as the DMs were.