That sounds like a lot of work.
My bank has a browser plugin that can create virtual cards with just a few clicks.
dispute the charges, get a new number. Takes < 5 minutes and I keep going.
This isn't the case for me, it would take me quite a bit of time over a period of several weeks to update all of the places i use my card if I were using the same number everywhere and it was compromised. I handle a lot of billing. I've had cards compromised at least three times in the past and it's very unpleasant. (for me)