You should be able to see enemy SS cooldowns by pressing tab.

The only reason they don't let you see enemy summoner cooldowns is because they want the game to be interactive, and have players communicate to each other if someone flashed or used teleport. But the truth is you can't always rely on your teammates to say enemy cooldowns and as a jungler as I pan through lanes I often see that an enemy flashed and my teammate didn't even call it out.

They changed the jungle timers so that they have always have the yellow timers before they spawn that are visible to everyone in the game. Before that change, it was a skill all on it's own, trying to figure out the enemy jungle timers. Now that skill is gone, but we have something easier to use and less of a nuisance.

I think that being able to see summoner cooldowns is not as big of a change as being able to see the jungle timers. In an ideal scenario with an ideal team in a decent elo, players call out every single summoner spell and tell you when it's going to be up again. The higher elo you go, the less of an impact this would have. It would have zero impact in competitive and very close to zero impact in high elo. Why make it more complicated than it has to be?