Revive is an archetype in and of itself for certain game modes and champions (see PhantomL0rd's Revive/Teleport Karthus, or Dominion as examples.) It provides interesting game play interactions for a handful of champions, and in Dominions case, it's become an essential tool. I feel as though it doesn't see a place in any other game play aspect simply because if there were changes to it to make it a "viable" spell, it would be too heavily relied on, and would heavily upset game balance.
Just look at first the addition of Barrier, and then shifts over to Heal. When Barrier was introduced, it made extreme aggression in lanes much harder to accomplish because it was a low cooldown secondary defensive spell that had way too much power. After the changes to Heal, we saw the same kind of interaction, except in a different scenario. The shift went from using the second defensive spell solely to protect yourself, to giving you the ability to save your support. This is why the meta shows its almost a requirement in bot lane.
I'm not sure how long you've been playing, but if you played at all in the early stages of the game, you'd know the extreme power of what was Clairvoyance. Taking Clairvoyance on a support was quite literally the only spell you would take. It was the main form of granting vision, which was key for spotting out objective and making picks. Although it isn't seen in play now due to vision being an extremity through wards and trinkets, we're starting to see a lot of late-game AD Carries taking the blue trinket in competitive play, which has the same effect as CV. Overall, Clairvoyance has been replaced by the blue trinket in terms of usefulness, and should be reworked into something else perhaps.
As for the other spells you have listed on the poll, Cleanse is still extremely strong and used quite commonly throughout all rankings and forms of play, Exhaust is a bit too strong right now with the damage reduction (Although it will be seeing changes soon, hopefully), and Barrier is simply being outclassed by Heal. Barrier would definitely be a strong pick if it had more overall value, be it in the shield amount or duration. The reason Heal is so powerful as opposed to it's opposition is due to it's permanent healing effect, whereas barrier shields you only temporarily. Not only that, but even though Barrier shields for more at early ranks, Heal outscales Barrier by a bit in the end.