Such a thing will never exist in League of Legends. Allow me to explain why (because Riot did actually learn from a mistake on this subject).
So, Karthus. His passive lets him cast spells for free for 7 seconds after dying, while being invulnerable. However, originally, if he got a kill while in his passive, he instantly revived at base. This created a completely overpowered 0 downtime Kassadin build, where you would run Teleport + Revive (just in case you didn't get a kill with your passive) and you would basically have 4 lives in every teamfight on your own. Die, revive, TP back, die, revive again. And this was BEFORE the homeguard effect existed.
Even if it were just reviving them at base instead of on the spot, a post-death revive ability like this would cause the exact same problem in that you revive whoever has TP, they TP back to the teamfight, and they basically have 2 lives in every fight. Your ADC ran Teleport and built Guardian Angel? 3 lives! You have a Zilean top or mid lane? Make it 4! It would be just too powerful. Champions are balanced around that death timer.
Even worse, Yorick's old ultimate used to make a copy of the target that they took over if they died. But I don't think they could cast after taking it over, don't quote me on that, though.
Let's put this through a scenario: you have Twitch and whoever this ally revive champion is as your bot lane. It's 50 minutes in. Twitch has Infinity Edge, Runaan's Hurricane, Statikk Shiv, Berserker's Greaves, Guardian Angel, and The Bloodthirster. He dies, gets revived by his GA, dies again, gets revived again by you on the spot. That's 3 lives. 3 lives that a late game hypercarry has to completely ruin the enemy team.
Why it's balanced on Zilean is because the enemy team can CHOOSE not to give him the revive. They interact with it. They can leave him on 100 health until it times out, then kill him. Or, they can kill him, then if his team doesn't protect him, kill the entire enemy team and then he has nothing to revive to to save him.
Guardian Angel is slightly different; sure, it's a passive. But, it's got a 5 minute cooldown. And by the time you buy it, you're probably only gonna get it off once or twice by the end of the game, because you can't apply CDR to it. Even the active item CDR rune is only for actives. It won't affect Guardian Angel or anything else.
Also fun fact: Zilean's ultimate used to last 1 minute and his W used to lower the ult's cooldown as well. That got nerfed again for that very reason: you couldn't wait it out; you couldn't wait to interact with his ult target so they didn't revive. And, if he spammed his W enough, he could have his ult on multiple people at once.