The misconception with the new Assassins
I think that while everyone realises why the goals of the changes were/are supposed to be, I don't think everyone quite realises the how/what.
The primary goals were: Increase counterplay Fix the 'Feast or Famine' issue that Assassins inherently had.
Now the how-what (the way or method Riot used to achieve this) are a little more subtle. To increase counterplay: This is actually more simple and clear than the rest, but basically it was delaying burst (Talon's passive requiring 3 abilities landing then an auto attack, LeBlanc's passive having a charge timer, Katarina's daggers having travel time etc)
Now as for fixing the feast or famine issue. From what I see there are 3 key things here. 1 - Give Assassins some form of Level Scaling. Talon and LeBlanc's passive BASE damages both scale with level, making them have a source of damage that is NOT SOLELY dependent on items/stats 2 - Provide Assassins with better waveclear. With an exception to Katarina (who I think just needs some minion dmg+ing), Assassin's were given better waveclear (well mainly LeBlanc but she was really the only one with pretty shoddy clear). 3 - Give Assassins something unique that only they can bring (a la LB clone, Talon roaming. Kat and Rengar were already pretty defined).
Now the most important thing is 2 and 3, and why they are there, important, fair, and what they DO. They are there simply because compared to Assassins before, they don't 100-0 instagib in under 1 second, i.e it's compensation. They are important because they become SECONDARY TRAITS to the assassins giving them more depth and reason to pick outside of burst damage. They are fair because they don't instagib anymore, the counterplay is there. What they DO is keep assassins relevant at all stages of the game.
Now I feel like these concepts are being lost on the misconception that "Assassins lost burst damage for nothing", which simply isn't true. While the changes for the most part were simple, they were very radical in changing how these particular assassins interact within the context of the game and players. Comparing them to how they used to be doesn't hold up anymore. They used to have only 1 single function; to kill squishies disgustingly quickly. Assassin's now can do so much more, and contribute in other ways.