That is actually the complete opposite of what the ban phase does in tournaments. You serious with that?
You might think that when a team bans a certain character, you limit possible choices, which then must lead to a more limited variety of teams (since there are less characters to choose from).
That makes sense and sounds good on paper, but that is not at all what actually happens in practice. In a tournament without the ban phase, teams will almost always choose the best characters in the current meta. With two teams of 3, you will see the same 6 characters chosen in 95% of the games played where the only variety is the combination. Competitive gaming will always lean in that direction and the meta game tends to stagnate once those best characters and pairs are identified.
What bans do in this situation is force teams to think outside of just best meta characters because those will likely be banned. So you are free to create team comps that compliment what you ban out from your opponent and have to be creative with what the other team bans out for you. What you end up seeing is a more diverse pairing of characters to fit different ban strategies. More diversity in pairings leads to a more dynamic meta game as teams try to adapt to the current meta game through different ban/draft pairings to stay ahead of the curve.
Limitations bread creativity. It's a stone cold life truth.
With that said, Paul, there should be thought into where the bans actually happen. I've seen a lot of MOBA's recently stagger the bans.
-1st team bans
-2nd team bans
-2nd team picks (1)
-1st team picks (1)
-1st team picks (2)
-2nd team bans
-1st team bans
-2 team picks (2)
-2 team picks (3)
-1st team picks (3)
something like that could work as well. I am very much against triple bans however. 2 bans are more than enough.