The true culprit to "high damage creep."
Let's start with this, the only masteries that contributed to this are the Keystones, specifically Thunderlords & Fervor of Battle. If you compare the masteries that give extra % damage compared to Season 5 and before, the % is around the same.
And obviously, there being too much Lethality in circulation. (Theoretically Lethality is still a lot worse than Armor Penetration, since you only start with 60% with 40% coming over enemy levels. The reason why it's so broken is because there's just so much more Lethality from items, runes, the precision mastery than there was armor pen. It's not that hard to get over 60 Lethality even after the nerfs when before getting ~40 was difficult during the armor penetration days).
Besides that, the REAL culprit is the increase of gold circulation. Think about it, first blood gold, the buff to shut down gold last season, overall increase in local gold from turrets, THE INCREASE IN AMBIENT GOLD. THE INCREASE IN INITIAL GOLD FROM MINIONS! (all except first turret gold got from the 5.22 patch notes http://na.leagueoflegends.com/en/news/game-updates/patch/patch-522-notes )
"But how does this contribute to damage being higher?" Trick question, because overall damage IS NOT THAT MUCH HIGHER!
Because you have more gold quicker, you get items faster! You know what doesn't increase? Your level and experience. Meaning that before Season 6, you would get your items later than you do now, but your levels would remain the same. Because you're getting more damage while overall levels being lower, damage feels higher because the lower your level, the lower your health pool AND armor AND magic resist (if you get MR per level).
You know what made me realize this? URF. Ambient gold is EXTREMELY HIGH in that mode (to make games shorter), but experience levels are still the same. People are reaching one shot potential so much quicker in this mode than in normal Summoner's Rift. A level 7 Fizz in URF will have much much more gold than a level 7 Fizz in normal Summoner's Rift, and therefore more items and then more damage. Because the game isn't balanced around URF, the enemy laner will also be level 7 and still have the same amount of HP as they would in a normal game in Summoner's Rift, and die much faster because of the stat increase from the items.
The overall increase in gold in normal Summoner's Rift is also why you still get easily one shotted by someone who has a negative KDA, even though having a bad KDA doesn't mean you do 0 damage.
Plus, this proves that TANKS ARE NOT WEAK! There's a reason why LCS still has tanks in the top lane almost every single game!!!!!!!!!!!! They know how to farm with tanks and get leads as them. Watch LCS and watch what a tank can do in teamfights. Anyone who says tanks are "weak" or die too fast were probably behind and tried to facetank 5 people or was versus a tank shredder (Kog'Maw, Vayne, etc.)
Also, don't forget about obviously strong champions. (Jayce, Graves, Kha'Zix, Syndra, etc.)