People with the first three picks should get banning ability, not the last three.
Currently, in draft mode the last three players on your team are the ones that get to chose bans when it should really be the first three. Players who lock in their champions first are at a natural disadvantage because the enemy team gets to chose counter picks. For example, if the first player to chose their champ chose Taliyah, the enemy team could easily pick a champion like LeBlanc or Zed, who counter Taliyah pretty heavily. However, if a player with the last pick wants to play Taliyah but sees the enemy pick LeBlanc they can pick a champion that counters LeBlanc like Galio. The first picks need to be able to ban their specific counters to be able to survive.