Can The First Three Picks Instead of the Last Three Get to Ban?

Considering that they are the first to lock in a champion and the first ones to get counterpicked, I think they are more entitled to decide what gets banned and what doesn't. This way they can target ban and get at least some counters out of the way instead of just getting thrown into cold water.

On the flipside the last picks already have the advantage of getting to counterpick the enemy, which is especially valuable for laners, so I don't think that they need another advantage by getting to ban.

I for example never get to play my Yi, the champion that I'm most comfortable with, because when I'm first pick I can only really pick safe picks like Gragas, because everything else is definitely going to get counterpicked hard, especially something like Yi. I'd feel much more comfortable with getting things like Jax or Gragas out of the way to not get absolutely screwed when I want to play him.