I didn't play before mythics, so I can't say for certain, but a common consensus I've heard regarding the origin of power creep has been cooldowns. Partly due to ability haste removing the previous 40% cap, partly to assassin items being frankly overloaded with it and finally due to just the straight reduction of a lot of them. An infamous example for the latter would be Leona's Q going from 12 to 5, even though that was a while ago.
Designers and the balance team are also to blame, though not singularly. Having lower CDs and higher ability uptime feels cooler, which is a factor that designers and even higher ups are aware of and increase engagement - even though it results in higher DPM and much harder survivability for anyone immobile