Except PayPal has no FDIC protection.
The part of the bank (or credit union) that required the US government to provide FDIC protection was due to dealing with cash. Imagine creating a country with just electronic money. What purpose would a bank with a FDIC protection serve if the government can just operate electronic money accounts itself? And if you want to take more risk and earn a higher return, you find a broker or investment fund or investor.
Investing customers money, create money.
Most money in the world is digital already, there are many banks that don't have physical presence and traditional banks are shutting down branches more than the open because branches are just the foot soldiers. There are also countries where cash is almost not used. Banks are not about cash, they are about credit.
I don't know what a "physical bank" means though, AFAIk there's no such thing and the buildings that banks own or operate would serve functions like hosting employees/clients/systems but they might choose not to have some of those.
And they can do this without a federal government backstop, just like an SP500 ETF does or a US Treasuries mutual fund, or an REIT, etc.
My point is the federal government need not provide a subsidy to these businesses that "invest" customer's money (or simply handle the underwriting of loans in many cases).
Right now in the US, via the Fed Funds rate, the federal government pays a business 5.5% just so the business then turns around and pays me 5.05%, all for keeping an entry in a database. And these businesses pay a lot of less discerning depositors a lot less. Surely the federal government can just give all 5.5% to people directly.
The problematic part starts when someone acts outside of this structure, like employees who take customers money and invest with it without explicitly having a right to do that.
It impossible for a bank for example to put all their money into Dogecoin because someone got a hunch that Musk will tweet about it. To do that they will need to create some kind of instrument that allows others to bet on Musks tweeting habits.
> There really is no need for the charade of banks now that electronic databases are very solid technology. Their whole role in transmitting and keeping an account of money is surely reproducible
That's not what banks do. You can do that without being a bank, like PayPal did. Most places will have different and much lightweight regulations than banks for this and you will go to jail if you do anything more than holding and transmitting customer money.