There is no universal rule. Bank account-opening requirements vary by institution, account type, and entity age.
When banks usually do NOT require it
Opening a simple business checking or savings account for a recently formed LLC or corporation. Most banks accept the Articles of Organization/Incorporation plus the IRS EIN confirmation letter (CP-575) and the operating agreement or bylaws.
When banks usually DO require it
When the account is bundled with credit: a business line of credit, term loan, SBA loan, equipment financing, or commercial mortgage. When the entity is more than a year or two old (the bank wants proof you have stayed compliant). When you are switching banks and the new bank is doing fuller due diligence. When opening a merchant-services or higher-risk account.
The safe move
Call the bank and ask their business-banking team exactly what they require before your appointment. If a Certificate of Good Standing is on the list, order one dated within their window so you do not have to make a second trip.