So I got down voted the last time I said this: Unpopular opinion about Assassin damage
And related, Dive Fighter damage, and certain Burst Mages as well.
Perhaps the high-end Burst classes shouldn't be balanced around the ability to 100-0 a target. Now I don't mean they shouldn't be able to outfight certain targets or if they pull off a long chain of combos they can pull off ridiculous damage, but perhaps balancing them around the idea of swooping in and knocking out a squishy right in everybody's faces is a tad...silly. It establishes a terrible precedent for the game if the main carries can disappear in literally the blink of an eye.
"But TehNACHO, didn't the Assassin rework fail in part because Riot tried to force clunky delays into Assassin combos?"
That's really only one way to make it more difficult for Assassins to kill a target when there are multiple little tricks that should be considered. Let's consider some scenarios where it may be justifiable for an Assassin to successfully 1v1 a target, outduel them, and otherwise not gimp them entirely as a class. One example I can name off the bat that already exists in the game is Kha'Zix's isolation damage. If you're caught running around alone by Kha'Zix an Assassin, you should die for that. Another example may include massive and/or guaranteed damage on champions with low HP. Evelynn's Ultimate execute is fantastic given how relatively slow her upfront burst can be (factoring in charge time for her charm). Duskblade of Draktharr used to have a Passive called Nightfall, which would deal %Missing Health damage after a two second delay after auto attacking a target. Perhaps Assassins shouldn't be balanced around 100-0'ing targets, but basically guaranteed to 50-0 somebody, if that makes sense.
And there are niches that can exist outside of 1v1ing a target. Much of Talon's design approaches this. With not bad waveclear from his W and Tiamat being a core item on Talon, as well as the function of his E, Talon very easily occupies a space of being a premier roamer. This allows him to clear waves quickly, maneuver easily around the map, and start skirmishes at a number's advantage with relative ease compared to many champions in the game. Invisibility from Evelynn, or flex roles like Kayn also fit the bill of adding a unique dynamic to the Assassin class that absolutely doesn't require the ability to 100-0 a target outright.
To deal with this without another Class Rework, I think the game actually needs more Lethality items tailored towards Assassin strongpoints, but each individual item is either only situationally strong or at least in general weaker than what we see today. We can pull the ol' Frozen Mallet/Ashe here and borrow passives from existing Champions and implementing them in items, like Kha'Zix's isolation ability. We can look towards more experimental designs like Staff of Flowing Water, Mirage Blade, Trickster's Glass or Netherstride Grimoire from Black Market Brawlers to see some funny ways to play around with unconventional mechanics that an Assassin may be able to use. We can give AP Assassins and Burst Mages their own dedicated item pool. I actually think limiting Assassins to 3 Lethality items or sharing with other classes makes them far more...well, not one dimensional and binary, but I honestly don't believe anybody is happy that you more or less build the exact same items to get the exact same results on what's supposed to be a wide and diverse class of champions.
The best modern example of Assassin design I can give is Pyke. One only needs to watch a Pyke montage to see how ridiculous and fun an Assassin kit can be without having an overwhelming 100-0 rotation. With his Ultimate being a premier execute with a reset, and due to the functions of his Hook and Stealth, he really plays the role of picking off targets and snowballing fights in his team's favor. On the other hand, because his Stealth is only Camouflage and his dash being just as (if not more) valuable going into a fight than going out, not to mention his lack of defensive scaling, this all means that Pyke is really playing serious games of risk and reward if he wants to start a fight or dive into a chaotic teamfight. To rephrase, he's kinda actively dissuaded from jumping in on a full health target surrounded by teammates where other champions might try to force themselves in and still succeed to burst somebody down. Not to mention because of his HP to AD conversion, he interacts with items way differently than other champions. While this isn't the same as giving Pyke a dedicated item pool, it does shape his build to be far more unique and situation based than most other champions in the game.
Now I'll admit most of this post is targetted towards assassins but I do muddy it with Dive Fighter and Burst Mage problems here and there. If there's any clarification needed, please feel free to ask.
tl;dr: Assassins need a niche outside of 100-0'ing people. Part of this can be achieved through interesting niches some of which are already (partially) capitalized by existing Assassins. Part of this can be achieved through introducing more dedicated Assassin items, where perhaps each individual Assassin item isn't as strong but allows for Assassins to build for the situation. Pyke is a super cool Assassin.