I wonder how this became a problem. Your CC number is not just 16 digits long. It's 16, plus expiration, plus the 3-4 extra security digits, plus your name, plus your zip code. That's quite a lot of entropy.
That's not true. The number is just the number, though it can be more than 16 digits. The initial six digits identify the card issuer. Expiration and CVC/CCV are security checks, but only work in combination with the number. Name is generally not verified, though is often used in fraud assessment. Address verification is uncommon, and almost unused outside the US.
Billing address verification is extensively used in the UK.