This is becoming more and more common from issuers. BoA, Chase, and even Venmo Credit have this or similar functionality.
I suspect that major banks/credit card companies don't like this service because it brings in no revenue (at least directly), takes resources to maintain, and arguably encourages some of their customers to engage in fraudulent-adjacent behaviors using virtual card numbers.
I've avoided services like privacy.com because I am weary of giving a third-party access to my credit card for this purpose, so I do wish more banks/credit cards would offer this service directly.
Their extension, "Eno", is available for both Chrome and Firefox.