Can we have 5 bans per team?
The biggest issue with this is that an average LoL player likely isn't going to have a very big roster to fall back on. Usually players don't start getting cozy with a wide selection until they're ~diamond from what I've seen, which makes more bans considerably more detreamental to players with fairly small pools. Each champ requires a significant amount of IP to unlock, and they require a significant amount of time to get good with as well.
Even at the pro level, most pro-players have a fairly small champion pool where they can play at a pro level. Being able to ban out 5 champions would easily allow pro-teams to turn 1 challenger player on the opposing team into a diamond V player. While each team usually has 1 player you just can't ban out, there's usually 4 guys you can.
we've had 3 bans since s1 and you have released so many champs. theres not enough bans to deal with the constant "problem champs."
And there never will be. Even With 50 bans you'd have ~65 problem champions.
There has always been ~3 top-picks for each of the 5 lanes, for ~15 must-pick, must-ban champions. I'd say that has everything to do with gold, silver, and bronze medals, 3 being a solid number of counting, and people being to lazy to keep more than 3 champions in mind for a specific meta.
If you look at win rates or any data-tracking site, there is no valley in power between "problem" champions and other champions, it's just an incredibly smooth gradation of very finite, minuscule differences between champions that only a pro-player focusing on exploiting every minor 0.005% advantage is really going to properly take advantage of.
Likely the only thing to change the perception of an elite group of OP champions would be if Riot made learning the subtle nuances of each champion easier, faster, and more available to everyone - giving everyone the information to make fast decisions on more than 15 champions.
They could maybe pull that off with achievements that specifically encourage the core strengths of each individual champion, making it easier to remember what they bring.
Or just better champion bio information, like "this guy still hits really friggen hard while building full tank" or "this guy is much better in 1v1s than team fights".