Team Captain should be assigned to most honours
First and foremostly, the entire team captain system is dumb and should be replaced with one ban per person, both because it will be faster, and because it will allow for less RNG. But Riot probably will not go through with removing it since <Memes>.
Anyway I suggest you at least remove some of the RNG involved in it. It's quite annoying to play a game where your team captain will refuse to communicate and ban three people in their lane, even worse if they do poorly afterwards. Bans are Vital to draft pick and all of them shouldn't be risked going to a troll. So instead of having the team captain be decided by random chance it should be decided by whoever on the team has the most honour ribbons since its a lot more likely they will communicate. It also gives a purpose to an otherwise forgotten feature.
Now one thing I want to make clear is I do not want the Ribbons to decide pick order. That should still be randomly decided, instead the person banning should not need to be in the top slot and could be Summoner two, three, four or five.