Why does Ekko get a free GA + damage?

It's his ultimate

That's like asking why Malphite gets a free Dash+Damage+AoE stun/escape

GA works while stunned, Ekko ult doesn't

Because it's balanced

It's not free, it's his ultimate that also takes mana.

Why does Shyvanna get free flash+damage?

Why?

why does zilean get a "free" ga ecks dee

It's his ultimate and other champs have their ultimates too.

The GA + damage isn't a problem because he can't have both most of the time. If he managed to have both that's his outplay.

The champion was broken because of the tank build + E, not because of his ultimate.

It's not free, it cost 100 mana and has a cooldown.