Really interesting. In theory, I'd prefer having a smaller chance of a less debilitating negative consequence tied to each "over-limit" use of the PC's resource. "Full recovery" and "exhaustion" are big chunks which create a risk 'cliff' and a reward 'spike', but it does have the distinct advantage of being much less fiddly than a more incremental approach.
Our recovery mechanics are a little more complicated than that - there is a substantial difference between recovering LR abilities and SR abilities.
Just as an example...
Fighter (Level 1) expends all his SR abilities and pushes himself to recover them again.
He auto gets them, but rolls a check. First recovery of the day and it has been 2 days since his last LR so the DC is set at 5+2 = 7.
His modifiers are 2 x proficiency, therefore +2 x 2 = +4.
He needs a 3 (3+4 = 7) to avoid gaining a level in Exhaustion.
He succeeds or fails, the next DC on that day is increased by 5, therefore 7+5 = 12
We have a further rule, that applies to SR & LR abilities as you roll for them separately - if this is the first time you are attempting to recover abilities since your last LR you gain Advantage on your first roll.
A wizard wishes to recover his LR spells slots (same level same day).
He auto gets them, but rolls a check.
The DC for LR abilities is 10 + the number of days since his Long Rest therefore the DC =12.
Wizard rolls +4 and has Advantage (since it is his first time recovering). Needs an 8 to avoid
3 levels of exhaustion.
Should he wish to try recover LR abilities on the same day the DC increases by 10. ie. 12+10 = DC 22.
There are more rules, provisos...etc but this is the basics, I can send you the full doc if you want.