My wife and I bought a motorcycle a few months ago. In the office at the shop we counted out the thousands of dollars in paper money. I don’t need anyone’s approval to pay my bills. The motorcycle shop did not call the bank.
I do need someone’s approval to pay my bills with their money, like a loan or credit. I use credit to get the cash back bonus, I don’t need credit, I use credit. I don’t pay interest, I earn interest.
Mostly the permission and trust flows the other way. I give the bank permission to pay my bills and I trust them with some of my money. I don’t trust them with all my money. Banks are no more reliable than the power company or your internet service provider or your cell phone carrier. They might have outages or go out of business.
Where is the use of banks mandated by law? Using banks is totally optional. It is a convenient option, convenient to the point of irresistible but it is not required by law.