Before the cooldown it was great for the AI because on high difficulties Mongolia would annex like 4 cities within the first 100 turns and snowball out of control form there.Remember how strong his UA was when it wasn't on a cooldown. It overperformed most of the time as long as it had city-states to heavy annex. Even when it didn't have a cooldown, them having a fight on city-state borders suddenly had it be annexed out of nowhere. Having it be restricted to a Sphere of Influence is just nerfing Mongolia. 8(at most considering the current cooldown) Sphere of Influences isn't as strong as 8 free cities. Not to mention Sphere of Influences don't work pre-world congress code-wise, so that idea is thrown off the table.
Unless suddenly we want to establish Permanent Alliances with City-States outside of Sphere of Influences, then that's a different detail to discuss on.
I don't think the cooldown even affects humans because I've never tried to use it more than once a game.