High character popularity and unfun mechanics may not be bad for game balance, but...

They are bad for game health, especially when combined.

Riot has defended both high playrates for certain champs, and unfun/unfair mechanics like Yasuo's multiple safety nets during his "weak" laning phase and Fizz's troll poll in terms of game balance. They may be correct that even something like invulnerability on a 5 second cooldown can be implemented in a way that is "balanced", but these things are bad for game health

Unfun/unfair mechanics are counter-intuitive for game design, their existence dis-incentivizes playing the game, why would you cue up when there's a chance that you'll have to fight a champ you will have no fun playing against, even if you win? High popularity that persists more than your average FOTM, such as Lee Sin or Thresh being at 10%, 20%, 30% or more leads to the game being stale, where, in a game with 120+ champs, you're seeing the same thing over and over.

These two factors may not be very bad on their own, but when you combine them they create a situation where people are being driven away from the game. When that chance of the game not being fun because someone picks a champ that's like getting teeth pulled goes up to a almost 1 in 5 chance or more like Yasuo in midlane, or Thresh/Vayne botlane, which is almost at 2 in 5 chance, why would anyone want to play when there's such a large chance of your 25-50 minute game being just a shit experience?