Make it so teammates can't ban the champion you have hovered.

No

There is one reason why this isnt so good idea.

Lets say there is champion that is really broken, lets go with Twitch. He got some super big buff for who knows why and now if you pick him it is insta win for you. So you want to play Twitch so you select him and told your team not to ban him, but enemy team has a first pick and they pick him as first pick. So, now enemy team has a champ that your teammate really didnt want them to pick.

It is little extrime exemple but I hope you get a point

I actually agree ... I don't think your teammates should be able to ban the champ you hover.