Riot wants the game to end sometime, and allowing champions to become invulnerable does not cause the game to end.
The average game is also 33 minutes from what I've seen. Maybe it's balanced around being 3540 minutes, but from everything I've seen, experienced, played, and watched - you shouldn't be getting full-build in your average game. 2 core items and working towards a 3rd is more where you should be, let the game drag on to long: and late game champions are gonna be late game champions.
Also: when your allies get more and more damage compared to everyone's defensive capabilities, a 2 second stun means bad and worse and more awful and awful things for your opponents. Stuns/CC also get more powerful the more people can capitalize on it - a 2 second stun when you're by yourself as Leona means a very different thing than a 2 second stun when you've got 4 allies and a tower on your side.
A solid tank-play on someone like Leona can demand you live for ~30 seconds in the early game, where late-game you can make game-winning plays with only surviving ~3 seconds. It's entirely possible to be tanky enough to make game-winning plays on a tank while dying very quickly comparably to other phases of the game. The important thing is how tanky you need to be to get your job done - it's not just 30 seconds flat the entire game.