Most private banks aren't established by an act of Congress and run by people appointed by the President and approved by the Senate.
In order to be bailed out, which is a necessity, they even need contacts as high up as the president.
And even that is ignoring the long history of the government making specific laws specifically to benefit or destroy a single bank.
Nope, no government role here at all. This division simply results in privatizing the profits, nationalizing the losses in trade for having politicians name the owners.
it is if you want to be a reserve bank of course, which is why anyone wants to have a bank in the first place.