Why can't a credit card company stop monthly charges from posting to an account after the account has been closed?

Cancel an American Express account. The following month charges appear when a company (in this case AAA) tries to renew my membership. The account has been closed but Amex tells me to get the charge reversed.
Same for the monthly debits for a newspaper delivery. Why doesn’t Amex or Visa or Mastercard just reverse the charge and take a debit from their payment?

Same thing for wireless charges? Why do they accept charges from third parties where you (the customer) has not authorized the charges and why is it the customer’s responsibility to get the third party (who is often reluctant to do this) to issue credits against the charges?