Perhaps others are more organized than I, but I find that I don't remember all the accounts where I've stored my CC info, hence having the CC company continue recurring payments is a convenience. Usually, I've then gotten an email telling me that the continuing payment was a one-time courtesy and that I need to change the info with the vendor.Mel, I am right with you. I don’t think this should be done- it should be up to the customer to go to the payers and give them the new card number for recurring payments.
I think I’d file a complaint with my State Banking Authority. What’s the point of reporting a missing or stolen card if they are going to put recurring charges through?
Just the other day, I got an email from Citi that an online payment for the small sum of $7.05 from Walgreen's had been rejected. Since the charge was not mine, I was able via the Citi website to cancel my card and request a new one. The website even told me what the new account number is and the 3 digit verification code so that I could use it immediately. The next day, I got an email from Samsung Pay that Citi had reported the new number to them and that it was all set up. I found it all to be efficient and convenient and I did not feel that my security was jeopardized.