I used to think this was needed but I've since changed my mind.
Three bans really makes the most sense because it creates more opportunities for counter play and strategy. If every lane could ban their worst counter that just seems like too much. As it is you have to decide what lanes / positions you want to focus on. I don't think more bans would add to the depth of play.
Not to mention four bans means that in highly competitive play it would be easy to completely shut out players with smaller champion pools.
Besides though I feel like the meta is a little too stagnant (in NA at least) and too many players focus on tier lists the amount of champions may be irrelevant because not every champion is viable in every situation. There are really good situational picks that would suffer to more bans.