I don't think I want more bans. In some ways it makes sense - as the champ pool increases, you should be able to keep a similar ratio of the champion pool banned out. So theoretically it should increase as the number of champs does. But I find the way bans are currently used by the community has some really bad problems that'd need to be addressed before any increase in the number of bans happens.
Look at Sejuani for example. There's very little data actually suggesting that she's overtuned right now - her winrate's gone down to a regular number and her competitive play has completely disappeared - so what's causing people to ban her at the moment? The fact that nobody has told them not to.
People ban far too much based on "I heard this champ was OP" and it leads to incredibly slow reactions in the pick and ban phase to balance - if Sejuani was locked out of the ban phase for a few days so that people could only pick her and then people were allowed to ban her again immediately after, I am pretty sure her ban rate would go into utter collapse because people would learn that she's actually fair to play against again. But right now (with most champions, not just Sej), people are far too happy to just ban a champ in every game because they heard they're OP and because they never see them as a result they never actually learn how to deal with them. It's the same with LeBlanc. She just got dumpstered and her ban rate is still 30% because a lot of people haven't actually found out that she's shit now. Her ban rate should be collapsing but it's a slow drop off as people are just happy to use the ban phase to ignore her existence in the game.
If the ban phase gets reworked or people get more educated as a whole in the future then I'm happy for the number of bans to increase but as long as people are so content to just ban the champs that they heard are OP and are so happy to use the ban phase as a way to escape learning how to play against champs, I'd rather not. All this increase would do is lead to people who ban the same champs every game being able to add one or two more perma-bans to the list, while it wouldn't do much to benefit the people who try to use the ban phase for its intended purpose.
All this change would do is add like 20% to the ban rate of every currently highly banned champion because people just use bans because "ugh Katarina is cancer". And if you want more bans so you can more easily ban out counters to your strategy... you don't deserve them. You should have to choose between which counters you think are most dangerous rather than being able to ban out everyone that could possibly pose a problem. There's nothing to be gained from more bans right now.