Transaction clearance between customers at the same bank don’t involve any central authority. In fact banks are reporting their net transactions between each other aka if A has 100,000 transactions for 100$ each with B that sum to zero net transfer they don’t need to report anything.

This is needed as otherwise banks could claim to have unlimited funds.

Bank notes provide privacy and are created on demand. Having 1:1 bank notes to M1 money supply would simply be wasteful.