%hp damage occurs when you want a champion to deal damage no matter what, an assassin for example, his only job is to kill the target he chooses and then be useless for a while (best case, of course), by giving him/her %hp dmg you make sure that no matter who they're hitting, it hurts, a lot.
Now you gotta look at the constrains these skills has, in ekko's case he's %hp AFTER 30%, also it's MISSING hp, this translates to enemies like this: DO NOT fight Ekko when bellow 30%, you won't win no matter what. And it translates to Ekko like this: go after the one with less than 30%, you'll kill him for sure.
Sadly, Ekko has such a kit that allows him to bring someone down to 30% very easily, making his best case scenario really overpowered, if E did no damage at all, Ekko would probably be balanced, considering the fact that he has 3 slows and 1 potential stun/shield, he doesn't need to be overloaded with magic damage everywhere.
Fizz is even worse, while his %hp dmg is cooldown constrained, with 40% cdr it's 6 seconds... and the skill remains active during 6 seconds... meaning that with enough cdr Fizz efectively can mantain his W on forever, that said, %missing hp damage becomes seriously good after 50% hp, so in reality you shouldn't activate it before that BUT on fizz' case it has a base damage attached to it... plus it is enhanced by his ult and once again, his kit allows him to bring you down to 50% hp without much effort, just hit your ult and you're on your way.
tank versions of these champs are subjected not only to their %hp dmg, since as you noted yourself, the likes of Zed and Vayne has this type of damage, it's just that Zed and Vayne are balanced around scaling, while Fizz and Ekko just have huge bases and even damage/utility where they shouldn't and current items allows them to abuse these strong points.