I think PD2 handled it best. Each class had a sort of teleport added but they had cooldowns. And before you say cooldowns don't belong in D2 the game has plenty of cooldowns. Unlimited teleporting with no cooldowns make for some boring end game parties due to players jumping ahead killing champs by themselves etc. And it's fine if players want to split to mf and kill mobs by themselves, but the speed that teleport allows makes it ridiculous creeping into D3 territory. If you check any split shard tz game pre teleport you know what I mean.
If they fix teleport and it's own items need a limited number of charges even if it does recharge over time or via cube recipe. We had a version of the game pre-teleport (excluding sorc) which was still tremendously popular.
The player power creep since runewords were added along with telestomp make for a sort of boring end game. If anything at this point the game needs another difficulty or map system. I really enjoy runewords but combining them with teleport is kind of the point easily botting the game happens because it becomes so simple to skip or instantly kill everything. But everyone wants enigma, or "their teleport", because it's the only way to keep up with the other players telestomping in pub games taking all the champ packs.
i think cooldowns is not the answer on tele.
i think the could rework how much it cost.
for sorc, it remains the same.
for every other class:
cost a lot of mana per cast, like a flat % of their mana pool