As I say in my book How To Be Invisible, "Hundreds of thousands of American citizens, as well as a similar number of illegal aliens, manage to live without any bank account at all, and not all are financially disadvantaged."
This is one way to ensure that you do not accidentally reveal your home address by writing a check for the rent, taxes, home repair, or whatever.
Any normal purchases can be made in cash, including gas, car repairs, appliances, and even expensive electronics. If a few bills must be paid by mail, money orders can be used.
For convenience, of course, a bank account is important. Some use an account in Canada and withdrawn funds at ATMs. Others keep an account in a small faraway bank, as described in Invisible Money. And a few intrepid souls use the ultimate in privacy, a nominee account.