Most countries do have some kind of id number like that, but they always have a "password" too. In Italy authentication is done by the SPID providers[1] or with an electronic id card (or physically with an id card, driving license or passport).
You can't get a credit card and spend as much as you want in their name. You need at least a stolen or counterfeit physical document to open a bank account, or a stolen password and a SPID second factor to file a fraudulent tax return. In the US the SSN is often enough unless you opt into freezing credit.
[1] for non Italians, that's the acronym for public digital identity system; it's a SAML-based authentication mechanism used by most public websites including tax returns, pension/welfare, and healthcare
