Sorry for getting into the thread late and not reading all of it before posting...
Yeah. I'm not really sure what problem the Slow Healing variant is meant to solve. I think it fails on the goal of making players more cautious or plan more (outside of planning how to get around slow healing). Maybe it makes some folks feel like recovery is more "realistic," but I think this is greatly outweighed by the impact to the play experience as described by the posters in this thread.
The question still remains, what is the goal that is trying to be achieved and what variant rule or house rule could be used to make that happen?
I agree that the "Slow Natural Healing" variant purpose is not that clear. It generally only means less HP available during the day. With the standard rules, you have a minimum of ~150% of your max HP per day (because of the rate of getting back
half of your HD during a long rest). With the Slow Natural Healing variant you are guaranteed only a minimum of ~50% available (you get those HD back but not your actual lost HP). So yes, overall the game will be tougher unless you often have "empty" days with no encounters to go back to full HPs. But how that is different from having for example more monsters per encounters (or anything else than wears down your HP more) may be a matter of details.
OTOT the "Gritty Realism" variant has primarily the purpose to play adventures with very sparse combat encounters, perhaps somewhat LotR-inspired. If you have stories with sparse encounters, then this leads to either the PCs using very little of their resources or otherwise going "nova" and beat all the encounters easily (the latter however carries the danger that an occasional second encounter on the same day can spell doom to the group). In such campaigns, it makes sense to turn hours into days and days into weeks. Nothing really changes in resource management except the narrative.
If you use the "Gritty Realism" variant but do not change the rate of occurrence of the encounters, then it definitely gets
very gritty, as the PCs are strongly motivated to
avoid encounters as much as possible. This also makes the game more difficult for the players, so I am not sure if at the end this ends up a popular choice
A 7-day Long Rest period was too long.
When I first read the "Gritty Realism" variant, I thought that perhaps what they might have wanted is to grant to benefits of a long rest
every 7 days, but with the long rest itself still taking a single night. This would have made the variant more usable because it doesn't require to actually take a break from the adventure... but from a narrative point of view would have been probably breaking suspension of disbelief.
Probably, a middle ground could be found by allowing some partial recovery of resources, but this certainly leads to a more complex set of rules.
It also made explicit the idea for why Hit Dice exist in 5E as well as overnight recovery. Because my players constantly talked about how if they had the Healing Word and Cure Wound spells at their disposal, they would have just cast and cast and cast them over and over to get everyone back up on their feet, then slept, woke up, and just cast and cast and cast some more if it meant they didn't want to spend 3 to 7 days "resting" for a Long Rest. Which tells me that even if I was in a future campaign to make it such that the recovery of spells and class features remained a 24 hour "long rest" but that healing and the recovery of hit dice were kept to 5 to 7 days for a "more realistic slow healing" type of situation... the players wouldn't bother waiting. They'd just cast healing spells ad infinitum. Which truth be told, is pretty much exactly how we always played in AD&D, 2E and 3E as well. Screw long natural healing recovery times... just bust out repetitive Cleric spells or Cure Light Wounds wands.
I don't think it really works to apply the "Gritty Realism" variant rules to HP only but not on spellcasting, pretty much because of what you say here.