Getting a card cancelled is a massive inconvenience - not least of all because you're without a card for the short term - but then you need to update your payme

Getting a card cancelled is a massive inconvenience - not least of all because you're without a card for the short term - but then you need to update your payment details on every service you use (that isn't a direct debit). Having one place to enter your details is way more convenient. Plus you get the bonus of having an auditable trace (ie via unique virtual cards) of who made what payment. This would be invaluable if you then want to contact the business that compromised your details. For example in some instances they might not even be aware that they've been hacked - eg if they're running an off the shell solution like Magento but not kept up with security updates. So there are still some benefits to the aforementioned service even aside the topic of liability.