And there's just a lot of champions that quite frankly need bans.
if there's considerably more than 6, no there's not. You have a wide range of solid champions to choose from that are on a pretty equal playing field.
Also - the purposes of bans isn't to remove the most OP champions. It's purpose is more strategic - such as removing an excellent counter to your strategy, or just removing a champion you don't want to play against.
A lot of champions with the highest win-rates are considered terrible by the community, and a lot of must-pick/ban champions are in the bottom 15 win-rates. There isn't exactly a valley of power between the best and worst champions in LoL.
The balance is solid enough you can take a champion like Poppy into a tournament and still have a solid shot at winning.
On that note, a lot of the picks/bans are just a list of ~6 champions everyone to lazy to care about looking into why to ban just memorizes and churns out each game.
Also - while you can't ban out most niches anymore, there's the realistic possibility of banning a player out.
Obviously there's some pro players that can play a different champion every game and do well.
But there's also a lot of pro players that do really good on 12~3 champions, and just ~meh to awful on everything else. The more bans per-team, the more underwhelming performances we're likely to see in tournaments, and the less likely we're ever going to witness a game where a star player's best champion ever makes it through pick/bans.
Give 5 bans per team, and you could ban out the star champion of every single player.
Finally - bans take time.
Adding more bans means the game takes longer to start.
The average LoL game only lasts ~33 minutes. The longer and longer you take to get it started, the more annoying it is when things go downhill in the game. Rather than investing ~33 minutes to loose in a normal game, you can invest ~45 minutes to loose in a ranked game. Or invest ~10 minutes in picks/bans only for Scumbag Steve to leave right before the game starts.
DotA 2 actually has 5 bans per team. And an extra 1:30 of stalling time during the pick/ban phase.
Watching the first ~13 minutes of DotA 2 tournaments is painful because of that. So painful, 100% of the DotA 2 games I've watched thus far actually skipped the first ~5 minutes of picks/bans before commentary even started happening.
Then I got to sit through the regular picks/bans commentary LoL games start with.