My credit union doesn't charge fees to transfer between individuals. And they are transparent about what profit from my interest they keep in order to pay for everything. Unlike the "no fees" bank you are exulting. Third-party payment processor that my local government uses is charging people, it's a fixed amount per check ($2.50) or a rather steep percentage (1.75%). Don't like the fees, then don't pay property tax, because they charge the check fee even if you go in person.
Regardless of where in your world you live, people don't work for free. The best you can do is regulate how the fees and taxes work. Because at the end of the day it takes equipment and labor to make the system work. Someone or something is sitting around counting your money for you, accepting payment, taking on the responsibility and risk for transactions, as well as providing a host of other services.