[Unpopular Opinion]: Damage isn't that high actually...
...But rather there's too much emphasis on team compositions with high damage.
Why would i pick a tank on top lane when i can pick Yasuo, a champ that can duel and farm well, has a great combination of AoE hard CC + Utility + Damage + Initiation? Why would i pick Sejuani when i can pick Lee Sin for an close amount of hard CC + Initiation + Team fight potential, and can clear objectives much more fast? Why i would pick a tank support when i can pick a support that has the same amount of CC + more damage?
The problem is that damage comps are way too rewarded, they have way too much advantages and not enough disadvantages. Defensive champs are lacking of utility and overall team-usefulness. If you notice, most of the games have 45 high damage champions (Lee Jungle, Camile Top, LB mid, Rakan Sup and an damage carry); no wonder why the players feel that there's too much damage: they are playing matches where 8 of the 10 champions are damage oriented. Even if all damage was reduced by 20%, you still would be 32~1 shotted by the Katarina and Lee Sin.
Did the overall damage increased over the years? Yes. Did it became unbearable? Not really. If you played into 4 assassins back in the season 3~4 you would still be insta-bitchslapped, just like now. The difference from back there to now is that you don't lose too much for not picking tanks/wardens. The damage meta is too strong; either put more advantages for defensive comps or reduce the rewards for going full damage team. Nerfing damage will not do jackshit if you still can pick a assassin and kill an tank with only 2 rotations and have more objective power than him.