I will say though that to do this the game would have to decouple health recovery time from class feature recovery time. You really can't put spell slot recovery on a 7-day Long Rest time table, the game breaks down. I've tried it, and spellcasters just end up not casting anything because they know they're going to have to wait 7 days to get their slots back and they feel like they have to save their slots for something really important that might happen down the line.How 5E is played by most tables is why the "gritty" rest variant needs to be standard. No one is doing 6-8 encounters between long rests - they simply don't have enough combat in their game. So the design should recognise that, and make resource recovery slower.
Now if you want to add in a third rest type... so that you have a Short Rest be an hour, a Long Rest be 8 hours, and a "Recovery Rest" (or whatever you want to call it) be 7 days, and then move spending hit dice up to a Long Rest and a full recovery of hit points and hit dice to a Recovery Rest (while leaving all class features on their standard Short and Long Rest timetables)... you might be able to work it out okay.