The thing is, yes her burst is lower than other assassin's. Other assassins don't have the ability to use stealth like she can, dancing in and out of her shroud.

Exactly. So when they remove the ability for her to use stealth like she can, then it doesn't put her in a good spot.

But I see no reason why a high mobility assassin needs immunity under turrets.

Well, she doesn't get immunity under turrets. That's Fizz, not Akali.

The reason she gets the ability to extend her dive under turrets is because her burst is so delayed. For other assassins, like Zed/Leblanc/Fizz/Talon, they can just drop all their damage on you and then use their snapback/go invincible/hop over the wall. Akali doesn't have the ability to drop all her damage on you at once like that, and if she blows her ult to run away like Zed or Leblanc can then her damage drops significantly from that even.

While the winrates of those champs are fine, it often feels unfair and unfun to play against them. If they wanna balance that correctly, these champions should have distinct weaknesses aside from 'stick together as 5 and pray'.

Try actually playing these champions (they're called assassins, by the way). That way you can find out what their actual weaknesses are, instead of inventing silly ones to complain about!