Issuing notes allowed them to engage in fractional reserve lending, which would be prosecuted as fraud in any other industry that attempted similar practices
I think there's an analogous practice for ISPs, Gym's, Clubs and Telecoms. They all charge a subscription fee for their services but if everyone actually tried to use their service at the same time, they couldn't, because in all of these markets the suppliers over-subscribe their services. This allows them to be more efficient and charge less for their services. In the case of banks, they don't charge anything for most of their services and even pay us for keeping our money safe. Just as described in what you quoted from wikipedia.
I'm sure there are other industries with similar practices but they aren't coming to my mind immediately.
Regarding the emergence of central banks. They are largely private enterprises and could have been created by private industry had it had the foresight to do so. The greatest problem with our modern banking system is accountability. The banks know that the Fed will bail them out and bank customers know that the FDIC will give them their money back if the bank doesn't. This leads to banks with very low liquidity taking even greater risks with their customers' money. To solve this problem congress could bring back Glass-Steagal, raise liquidity requirements and break up bank monopolies so that no bank is large enough to hold our economy hostage.