But for you to regard HSBC as a suitable bank there is a very large fixed cost which has to be covered - just paying for the branches, ATMs, technical infrastructure, people, etc. which is going to be there whether you keep one dollar in the bank or one million. As a general rule of thumb in a free market you need to keep your revenues from providing a service broadly following the same pattern as the cost base otherwise you have one group of customers cross-subsidising another group (in this case the ones who have lots of money in the bank cross-subsidising those who have little). And this opens up potential for competitors with revenue structures more closing matching their costs to win away your customers with lots of money which drives you into a vicious circle.
Think it through with some simple numbers:
assume that the bank's costs are $500 per year per customer (for the infrastructure) plus 1% of the money they have with you. If you charge $0 + 2% of the customer balance ("charge" in this case by offering interest 2% below inter-bank) then customers with a balance of more than $50,000 will be cross-subsidising those with a balance less than that. When a competitor comes along and offers a charging structure of $500 per year plus 1.5% then high balance customers will start to move to them and the bank with the unbalanced tariffs will need to raise its 2% charge to maintain the same amount of cross-subsidy from a reduced number of high balance customer. This drives more of them away, and so on. Where the costs of switching suppliers are low significant cross-subsidies of this type are unlikely to survive long. They have only been around as long as they have in the banking market because many people (particularly those with large complex portfolios) find that the hassle of switching banks would be significant and put up with a less than ideal charging structure.