A list of characters with Broken kits and why their kits are broken.
Too much of a generalist in the role, when they are passable they end up suffocating the pick process by being too reliable a pick at all levels of play.
Putting something in a role that is contrary to what the class wants to succeed at will cause the class to either fail horribly or be absurd.
Tank stats eat a lot of budget, and trying to balance that with damage on a class that is meant to use range as safety as well causes issues.
There aren't a lot of good ways to deal with champions that are fairly tanky with incredible sustain, so these champions have all been absolutely destroyed because of it.
Without having fair resource usage, champions with particularly good abilities can become absurd very quickly when either the meta favors them or they can abuse an item.
Stealth like eve's is still a problem, and it will likely always be a problem.
Riot views all of these problems with a different lense however, clearly. they tend towards trying to buff and nerf generalists, let champs like vayne and yasuo get out of hand before trying to change things, and will likely continue to make things like kalista. And they will also probably make urgot, galio, and eve rot for the rest of the games existence, not being able to change them without radically changing them, and not being able to balance them in the fluid game league is. And sustainers will probably be bad for a long time to come, rito needs to fix the stat stick/niche item divide before these guys can be made fair.
Twisted Advance is THE MOST BROKEN skill in the game....also now that CotC exists, it is even more oppressive.
is up there, but missing from your list while having more damage than Azir has and utility to boot.