I don't think it will be easy for them to arbitrarily increase the fees. Many customers are price sensative and would opt to other bank offering low fees. The gov is regulating the banking industry and pushing them to eliminate unfair charges.
The major banks tend to act as a cartel and have similar charges.
This is not true. Banks are very competitive with each-other. The published fees that banks advertise are generally higher then the actual fees that effectively are charged because banks are pretty liberal about reducing/waiving fees when they are charged to a customer the first few times.
Banks do try to cross sell multiple accounts to customers, which makes them less likely to switch banks when prices/fees increase.