I despised needing CLW wands. I was happy they chose a narrative method for hit point recovery in 5E.
In what way is tapping your wounded with magic sticks not part of a narrative? I mean, it may seem like a silly, contrary-to-genre narrative, but it's not like it's just hand-waved or anything.
The problem is how this doesn't work for all narratives.
For some stories, healing up full just because you got a night's sleep will mess with pacing or challenge.
To this many say "so choose one of the optional DMG rules then"
But this, or any singular suggestion, misses the point.
Which is: you want rules that support different pacing during different times, often within the same campaign!
No matter what the rules say it will be a bad fit for many adventures.
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Unfortunately, having a game able to handle varied pacing in spite of fixed rest/recharge/healing times would require class and encounter balance more robust than the broader D&D fanbase is willing/able to accept (to judge from the edition war, anyway).
The other alternative is for the 'short' and 'long' to be undefined and DM-moderated, rather than fixed to a set number of hours which the DM can change from campaign to campaign, that way, nominal pacing can be varied without greatly distorting the number of encounters per short & long rest needed to retain some modicum of balance among classes with different resource schedules and something resembling challenging encounters. That's actually in keeping with 5e's philosophy of 'rulings not rules' and basic core mechanic of "tell the DM what you do, and he describes what happens," so it's kinda surprising they didn't just present rests as undefined, as whatever the DM judges is sufficient time to recover from the exertions of the current adventure to one of two degrees,.
Play could go something like:
Caller: "Wow, that was a tough fight, we better tend to our wounds and rest for a bit before we continue on"
DM: "You're not sure you have enough time, a goblin patrol could interrupt you."
Player 1: "I need to spend HD and get my Second Wind back. Either that or some healing spells."
Player 2: "No way I'm blowing slots on anyone conscious, let alone out of combat."
Player 3: "I could do with recovering some spells."
Caller: "We chance it and take a rest."
DM (pretending to roll dice that mean something behind the screen): "Whew, that was close. You hear a patrol pass in the distance but are able to finish a 'Short' Rest. Spend HD and recover whatever else you get for your class."