I don't think that's practical. In an industry with very few players, it could work, but there are tons of small banks, credit unions, and online banks. Do you really think the big banks could convince every single one of them to just accept their share of the pie and stop trying to compete?
There's many small banks like you say, but the impression I get (I have not done the research to back this up) is that the few really major banks (i.e. Bank of America) have a huge market share. Again, I have not researched this, but just from day-to-day experience, it sure seems that way.
Edit: http://www.cardhub.com/edu/bank-market-share-by-deposits/
According to this site, the market share of the top 10 banks is about 45%. Those statistics are not highly precise but it illustrates the point I am trying to make.