So how do we fix this?

In the days when we had interest rates it was possible to make money on transactions by taking the money one day and paying the invoice on the next day. Overnight the money would earn interest. This would be profit to cover the transaction. So a bank could make money moving cheques around for people, taking two weeks to clear back in the days when everything was manual.

So with electronic payment there is no human inspecting signatures and doing data entry. So why the merchant fees?

In a free market a competitor that just makes money on interest should be winning here.