I get my next VISA I will also have to cut off some or all of the 16 credit card digits so that someone who steals it can't use it.
The cards magstrip etc store the card number. Personally - its a rather small exposure window that the bank is responsible for.
If you were really concerned, I'd disable the physical card and only activate it when you want to use it... and use Apple/Google pay for the rest.
Same with Verified by Visa/Mastercard Secure... When was the last time you encountered VbyV?
I occasionally get Mastercard Secure. Usually when I'm paying an exceptionally small bill overseas (eg. $5NZD), odd ball overseas transactions or high value transactions (eg. $5000-$9999). Using Applepay with the same vendors don't tend to trigger the fraud protections.