As a Rengar, Akali, and occasionally Zed player, I feel...
... that assassins are a bad design, and probably one of League's worst "Pandora's Box"-es.
At a fundamental level, the idea of an assassin is somewhat unhealthy for the game. Regardless of whether they're weak or strong, they are bad for most players, and bad for the game on a whole.
Firstly, let's establish the basic idea of an assassin, just to have a baseline--- a champion whose design is focused around high mobility and damage. They use their tools to get in on an opponent and deal a lot of damage in a short burst.
They're feast-or-famine by design; when they're behind or played badly, they don't have the strength to secure the picks they need to have an impact, but when they're ahead, their mobility and damage allows them to roll over a game smashing anything that walks up to them in a group of less than five. And it extends to their balance, too; when assassins are underpowered or bad, they're basically unplayable without the sort of massive skill difference that tends to make champion picks completely irrelevant, and when they're strong, they faceroll through games leaving behind massive trails of complaints and outrage.
They feel bad, for everyone involved, except one side in one case-- the guy benefiting from or playing the fed assassin. Meanwhile, the other team has to enjoy at least one of their members getting instagibbed almost every fight, which often has very little counterplay other than binary item purchases (tell me with a straight face that Zhonyaa's is at all an interesting item in functionality) or CC, which assassins are inherently given the tools to avoid (i.e. Zed/Talon ult, Akali shroud initiations, Rengar attempting to avoid the whole thing entirely with ult plays), as well as the stress of knowing that any movement away from safety or response that moves them out from their base will be met with sudden assassin-induced explosion syndrome.
An assassin who's behind feels terrible for their team, though; the player gets to essentially sit through a game that they have no impact in outside of very lucky positioning and timing plays or the occasional Rengar split push, and their team gets to sit through a 4v5 where the "AFK" is still eating resources and feeding them to the enemy team-- on top of still feeling bad if they're able to get a kill.
Because, really; sudden explosions of damage aren't interesting or fun for anyone but the guy dealing them-- and I can point towards the immensely negative reception towards any rendition of "lethality burst" Shaco as an example of when it's not even fun for the guy slapping out numbers.
And maybe that's why, no matter what, assassins are a constant source of whinging. When they're behind or not advantaged in the meta, they feel like they may as well basically not exist, and when they're ahead, everyone else feels like they really shouldn't exist. And this applies to all of the other "assassin-esque" things in the game, like Twitch and high-mobility bruisers that can burst (or both, in the case of Kayn).
They even introduce itemization problems, too, because the items on both sides of their playstyles are just as frustrating (excepting Mercurial-- I'm sorry, but this game needs a BKB-equivalent "cleanse" item, with 40% cdr CC and displacements existing as they are); lethality items either feel completely useless or act as instakill nonsense that makes playing a squishy character completely unfun in the mid-game,
would only work with a functioning equivalent that Riot refuses to add, and
has to constantly bounce in and out of different balance extremes because it's either too strong on its unintended roles or too weak on its intended use cases. Meanwhile, on the other side, you have Zhonya's, an item that never has competition, isn't interesting to play against (push button be stasis wow), and is either necessary for nearly everyone in an entire role or not worth picking up for anybody.
And for other options, you have shield metas (which are terrible), tank metas (which have their own host of problems that can be summarized with "sejuani jungle should never ever be the most-picked thing ever again"), or the absolute wasteland that is that terrible Tristana/Twitch meta where anyone who wasn't a tank instantly exploded.
Nobody wants any of the pieces of the assassin puzzle except for-- you guessed it-- the fed assassin player. Nobody wants the metas that favor them, because damage explosions aren't fun, and nobody wants the metas that counter them, because infinite shielding and "you existed in an ADC's field of vision so you're dead" aren't fun either.
Whether or not there's a real solution to this is... yet to be seen? I mean, there's the catastrophic and basically impossible option of shoving assassins back into the box they came from, but that's not even a viable aim of discussion-- so, for now, we're stuck with a pool of champions that are a constant detriment to the game.
And the less that's said about Draven burst, the better.