Assassins are flawed in design and do not belong in league of legends
tl;dr assassins do not belong in league and should be transformed into other classes with a few exceptions. Assassins are a class under much controversy due to their toxic nature of killing people before they can react. Their usual lack of mechanical (Kit-specific) counterplay means that playing against assassins is usually an unfun experience. However, as revealed in the aftermath of the pre-season assassin update, assassins need this low-counterplay burst in order to do their job effectively, or else you end up with more bruiser builds so that they can stay alive while they kill people.
There are many other bad things about assassins. Some of their qualities do not fit in the team-game objective-focused league of legends. The fact that they do typically worse in teamfights. Their snowbally nature, and league is already fairly snowbally by nature. The fact that they usually do not bring anything to the table other than the ability to kill people. Even some of the most damage-focused champs in the game provide some kind of objective control, as Marksmen are usually the best turret-takers and dragon-killers by nature. Assassins do one thing and one thing only - Kill shit.
But the biggest reason as to why assassins do not belong in league, combined with all the reasons stated above, is the fact that their job is nothing special. Burst mages and divers provide the same pick potential while still allowing mechanical counterplay through either their lower burst windows or reliance on skillshots. These classes also have crowd control, with some divers having strong tower-taking potential, and usually decent teamfighting. It's because of this that assassins suffer from a lack of diversity between champions. Nearly all of them have similar levels of mobility and burst, and it can be difficult to come up with an actually strong reason as to why assassin A should be picked over assassin B. This is due to their requirement of high-end burst meaning that auto-attack reliant assassins cannot exist, and the requirement of high mobility.
It's because of all of this that pretty much all remaining assassins (with a few exceptions, like zed) deserve to be balanced into becoming more bursty divers rather than full-frontal 100-0 no-counterplay burst monsters. With their lowered burst, elements like better objective control and crowd control could be given to them. I think with a champion like Shaco riot is stepping in the right direction by making him more of a melee disruptor with more of an emphasis on his boxes, as I have never been killed by a Shaco in an overall unfair scenario since his mini-rework, and he now has more relevance in teamfights with his crowd control and mind games.