To be clear, credit reporting and tracking is not the only function of credit scores in the U.S. These functions do exist elsewhere and are often called "registries." They are not private companies, but instead public centralized institutions. Likewise, it is not possible for private companies to loan debt to citizens, even by proxy.

For bankruptcies and defaults, there are similarly court records from public institutions, which you give a bank access to. They cannot search these sources without your consent, though of course they will then not loan to you.