There's a process for some card providers by which merchants can automatically update their card details for recurring purchases. Visa calls it Account Updater and at least Braintree has had support for it for over a decade.
Well that would be super convenient for me. At this point I'm just slowly transitioning to always using my checking account number directly for payment since that is stable.
The risk with that is you have no ability to contest a charge. With a credit card, you can contest and the card issuer will do a chargeback to return the funds.
