I haven't had a ton of time to examine all of the classes, but doesn't the cleric regain uses of Channel Divinity with a short rest? I think most classes gain some fairly substantial resources with a short rest. Every class has a different balance of short-rest and long-rest powers, but a game with seven short rests per long rest will not favor a short-rest-focused class much more than a game with one short rest per long rest will favor a long-rest-focused class.
Why?
Or, more specifically, why wouldn't they already be, since that's already how they work with respect to short rests?
Its a perception of time and restorative strength.
If I'm adventuring in a dungeon and take a beating, I might take a 1 hour rest to blow a few HD, recover my 2nd level spell slot, or recharge second wind. If I'm REALLY beat up, I can hide in a room, stake the door, set watch, and 8 hours later go out again.
I can't do that with slow rests. If I get dropped to 0 because of a lucky crit, my team can't rest a day for me to recover. They have to blow hard resources to bring me up (spells, HD) that they won't see again for days or even weeks. If I get dropped on day six of a seven day journey to the Crystalmyst caverns, will they want to waste spell slots to bring me up or perhaps save them for whatever creature guards those caverns? Would if I get bit by a dire rat and get filth fever, are they going to go back the six days they traveled to get me to a cleric how can remove it? Will I MAKE the six day travel home? What if they kill the ogre guarding the caverns, but doing so are now out of HD and spell slots? They got attacked 5 times on the way here; why would they not be attacked on the way home? Do they camp in the ogre's cave for a week (unmolested) to recover their stuff?
Anyone who can recover even a portion of their power on a short rest has the advantage over one who needs a long rest. In the standard format, that isn't a big deal: a warlock refreshes his spells 1-3 times (if even) over a sorcerer, but if they take a beating and need their spells, they are both 24 hours away from full strength. In the slow rests, a weeklong journey to the Crystalmysts means the warlock recovers 6 times to the sorcerer's once, and if they are both beaten, they both can't just "camp a week" in the middle of nowhere to reset; the warlock has his magic back in 24 hours, the sorcerer at the end of a 14 day round trip.
Effectively, slow rests make every short rest ability "1/day" and every long-rest ability "1/adventure". Turn Undead? 1/day (no cleric in AD&D or d20 had a restriction THAT harsh on turn undead!) Every cleric would be saving their spell slots for Cure Wounds since you don't know when the next critical is going to derail your entire travel plans. Warlocks become THE best arcane caster (at will invocations + short rest spell slots). I wouldn't DARE consider using CR = party level monsters; on day six that's a TPK. Dragonborn become horribly gimped.
Sounds good in theorycraft, but unless your game focused on an urban center with short jaunts to the immediate countryside OR a boatload of houserules and dice-fudging, I wager the game would begin to change in unexpected ways.