Then they're not round-tracking. They work for one round and that's it.
Off the top of my head
Sleep - 1 minute (10 rounds) or until awoken
Hold Person - 1 minute, re-save attempt every round, also based on concentration
Fly - 10 minutes (100 rounds) also must keep concentration
Magic Weapon - 1 minute, concentration
Haste - 1 minute, concentration
Enlarge/Reduce - 10 rounds, concentration
Etc, etc, etc....
The only difference with this mechanic is that instead of specifying 6 seconds or 24 seconds or whatever, it's tied to a die roll so that it's between 6 and 24 seconds before you can use it again.
In some ways it's a spin off of a monster recharge mechanic, but flipped so that you know exactly how many rounds it will be before you can use the ability again when you make the first roll. In fact, I might use this as a variant with dragon breath weapons, would be wonderfully descriptive and add some tension to the combat as the party sees the breath weapon slowly recharging.