How are you getting money into this "FedAccount" does your paycheck get sent directly to it? Do you first send money from another bank? If it's the former option then real banks will have less money to lend, if it's the latter option then it's no different then using Zelle or any other intermediate.
Honestly what you want sounds exactly like what the Fed is building which is a common electronic exchange platform. I agree with the other points in that I hope this is mandatory to some degree.
> If people then want to invest their money, then they can make that choice individually.
I think you're underestimating how much such a service (if it accepted direct ACH from your job) would impact our current banking system. Companies would just bypass actual banks and send all paychecks to everyone's "FedAccount" that would be billions of dollars moved. Money in real banks is lent out, money in a "FedAccount" would/couldn't be (if banks have fewer deposits then they can't get as much money from the Fed). This isn't just adding a minor service for the government to provide, it would be a complete redesign of our monetary policy. A lot of countries wish they could have a banking environment as diverse as the US, it's a huge feature not a bug.