Take a look at this, it's a translation from a video done by the best soloqueue player in the world:
https://www.reddit.com/r/leagueoflegends/comments/8t776a/dopas_thoughts_on_current_meta/
There is no champion in the game who spikes at 30 minutes. Sure, there are champions who are strong at 6 items, but it isn't an outright spike. Most "late game" champs spike their hardest on 3 items(think champions like azir and crit ADCs).
Besides, it's not over at 20, they're over closer to 30. https://www.leagueofgraphs.com/rankings/game-durations
The reason it feels bad for you to play late game champions is that you don't farm effectively enough to actually reach your items. Don't blame the meta, especially in the depths of low elo.