And the purpose of this is to increase money velocity by providing loans. "Narrow banking" (having the government provide bank accounts) wouldn't work unless the government also provided business loans, which doesn't really make sense.
Separating the issue of private money from providing commercial credit risk insurance (ala CDS) should be possible.
I'm not saying narrow banks are worthwhile, but it's utterly insane that it's illegal for a bank to simply hold $100 bills in a bank vault on your behalf. It's utterly insane that banks are not just permitted, but legally required to lend out your money. And there's a minimum amount, too, because a bank that lends out $1 of each customer's money won't get a license.