I'll rephrase.  For example, Coinbase Wallet asks for your bank account information as soon as you sign up.  Is this the norm?  If not, what are better places to use?

Or for anyone else that cares to answer my initial question, let me word it differently.  I want to remain anonymous at all times.  That means opening a wallet, funding it, buying bitcoins, receiving bitcoins, and converting to cold hard cash so I can spend the money locally in town.  It seems this is not likely.  So, is it possible to be a bitcoin user without having a bank account?  If you don't have one, then what?