This is an interesting idea. The problem with a single lender is that it removes incentives for good customer service and (sometimes) good products. Monopolies, whether public (DMV) or private (your local cable company) are universally hated. It would be difficult to design the right incentives for the government to provide a good product.
I think the main disconnect is that deposit banks never operated as a glorified vault. Lending against deposits is supposed to be understood by anyone entering that agreement. I understand why it may be a surprise when you first learn about fractional reserves because it may not fit an existing mental model. Instead, it seems unfair that a bank can create money. But it's not. Money supply and money velocity is a term used by economists to describe how much and how quickly money exchanges hands. The world's accounting books, with all debits and credits, always sum to the same total: however much money the central bank has printed.
There are a lot of benefits of the current system (liquidity, virtual guarantee of withdrawal, conveniences). Your proposal would replace a system where you receive a small income from your deposits to a system that steadily decreases the size of your deposits; I think that would be a hard sell.
