The thing is, assassins are a class that should stay in a small representation, because the class is hard to balance
Riot created the Assassin Rework specifically to try and make the class easier to balance. If they are so confident that they succeeded in their goals, why aren't they trying out new Assassins? But even then, I'd say a part of the problem with the class is the small representation. There really isn't much choice to who you pick, which leads the class to be a "I'm just going to pick the one that's best," kind of class instead of a class where you have multiple choices depending on the situation. Not to mention the fact that Riot really hasn't made a modern Assassin design other than Ekko. I'd actually say that Ekko is a pretty healthy and fair champion, that is after they got rid of the tank Ekko playstyle. If Riot created more champions like Ekko, I don't think that the class would have as bad as everyone makes it out to be. Most of the Assassins in the game are just old and outdated. Talon was old and outdated. Kat was old and outdated. Fizz, Shaco, Akali, Leblanc, the only Assassin that's really aged well in the fact that he remained healthy was Zed. And even he has his own slew of balanced problems. Sure, the Assassin rework tried to solve these problems, but it ended up making most of the roster worse with very few champions actually gaining more counterplay while also remaining fun to play.
Not saying that Ekko was perfect of course, because his release was definetly flawed and his design has been flawed all the way up till the Assassin rework where he got probaby one of the best reworks of the whole class, because it fixed the main problem that he had. Yes, his design was flawed, but saying that Riot's newer releases often aren't flawed is a lie. Think Rek'sai, Azir, Kalista, even champions like A-Sol, Camille, and Taliyah that were also pretty flawed. I think that if Riot actually tried their best to make an Assassin with a modern design and counterplay, they could have a really good champion on their hands. And no, I don't think Kayn is that champion. While Kayn can be played as an Assassin, his kit is designed in a way that the same basic abilities can be useful as either a strong-sustain duelist bruiser, or a roaming assassin, with only slight tweaks to the spells. Therefore, there has to be a compromise in the sake of game health for this kit to work.
That being said, I won't deny that Assassins have a game health problem and are difficult to balance, but I'd also say that several other classes in the game that also have big balance problems. Look at Juggernauts. Since their conception, they've only been either really weak or really strong. Right now, the only good Juggernaut is Darius who has his own slew of game health problems that I'm not going to talk about here. But just look at the other Juggernauts. Almost all of them are weak or just outclassed by divers that can do the same thing but also have more mobility and hard cc. But despite that, Riot has just released Yorick a couple of months ago, and are planning on releasing Urgot, who is going to be made into a Juggernaut as well. They are also making several big changes to Cho'gath to push him into the role of Juggernaut. Or what about the class that I feel like is the most problematic in the game, ADC. Now I know that I'm going to look like a whiny ADC hater for saying this, but hear me out. ADC's are the only class in the game that deal incredibly high sustained damage that comes from a point and click ability from ranged. This design leads to a lot of designs that feel samey. Champions like Twitch, Ashe, Sivir, Tristana, etc usually only have one main ability that sets them apart from the others, and other than their main ability, are pretty similar to the rest of the class. They usually have one utility or cc spell to defend themselves, and an attack speed steroid. There's really no counterplay to an ADC kiting you other than kill the ADC first, which isn't healthy counterplay and leads to classes like Assassins feeling either bad to play, or unfair to play against. But ADC is also the only class in the game that is mandatory in professional play. No other class can seige towers as well and as safely as the ADC. The only class that comes close is the mage, but unless your name is Ziggs, ADC's are going to beat you in tower-taking ability, even when they are considered weak. Because of the fact that they are mandatory, they are always going to be played, even if the class is really weak. That means that one person on each team is probably going to be having a worse game than everyone else. Therefore, Riot needs to overbuff the class in order for the class to be enjoyable to play, because there really isn't an alternative. Of course, this leads to a more frustrating gameplay experience because the ADC is lacking in strong counterplay late game, and games become a mater of which botlane feeds the least. I feel like ADC's like Jhin are a good start though, he is actually gated by cooldowns on his auto-attacks, and the rest of his strong abilities are skillshots. Other than him though, they just released Xayah, which has the same problems as the rest of the class. And of course, they are not going to let down on making new ADC's, nor are they ever really going to fix the problems listed here. I just don't feel its fair that Riot constantly makes ADC's which are a problem class, but they ignore making new Assassins which are also a problem class. I also feel like the Assassin rework was one of the worst class updates they've ever did. They didn't fix the problem that Assassins had (They were only good at one thing, killing squishies, and didn't have anything else to do other than that. There's no reason to pick Assassins over Divers other than the Assassin's ability to snowball.) and instead made it worse by removing the one reason to pick Assassins, and that's their ability to snowball. They didn't give Assassins anything in return that was actually useful, and because of that, the problems of the class as a whole were elevated to new heights. They really need to make a new Assassin update that actually gives Assassins something to do outside of killing people. Maybe some kind of objective that Assassins are especially good at collecting, or maybe Assassins have some kind of strong utility spells, like having better vision control than most.