Central banks may be useful in preventing banking crises every ~20yrs as happened back in the 1700s and 1800s. But even that’s not a certainty since the two most severe banking crises in history - the Great Depression and Global/Great Financial Crisis - happened under the watch of central banks. Some even argue the latter occurred because of the central bank keeping interest rates too low too long.
One benefit of central banks is to depoliticize monetary policy by moving it away from the Executive Branch, and giving it a consistent, Congressional mandate that it must prioritize in its policy and operations - low inflation and high employment. That’s probably one of the few indisputable advantages they have.
As for whether inflationary or deflationary money is better, I don’t know. Both have their pros and cons. The more I go down rabbit hole on each of these, the less decisive I am about it. But this website makes a comprehensive case for deflationary money, fwiw: https://wtfhappenedin1971.com/
