In Portugal we have had this service for many years and it works regardless of the bank (https://www.mbnet.pt in portuguese). Most people I know always generate one of these cards for online shopping, it's safer and easier to control.
That's indeed true! Although you still have the limitation of only being able to generate virtual credit cards of the same type of your "parent/real" credit card. For instance, with a Maestro/Mastercard you cannot generate virtual VISA's.