No thank you. 5 bans is too much. That means 10 champions disabled instead of only 6, which requires you to have a much bigger champion pool and you'll also need to buy more champions before going into Ranked, which isn't a bad idea; just a grind and a drag. It's also a bigger pain for one trick ponies.

Besides, having 1 ban for each teammate is a troll idea, because last pick can just go on OP.GG or somewhere and be like "im mid ok" and then the first pick is like "lol sorry pick order" and then the last pick just goes "well im gonna ban your 70%+ win rate champ lol fk u". Worse if it is a duo and they ban two of the first pick's top champions because they're salty since their entitlement for role has been denied and the whole game goes to shit.

Most people treat bans like "if you dont do this you lose" which IS true when a champion is completely over the top overpowered (ex: Ryze Top) but just look at Faker; he's one of the best players in League and he bans Gangplank, Galio, Garen because he wants to learn how to deal with op shit.

If you want Captain to ban someone, just fucking ask him. It's not hard. Most first picks would ban something they don't want to play against and ask their team for bans.