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As far as I know, the database is owned by the USPS, and they can't do their job _without_ that information. You can dislike Brave for buying access to the information, or dislike USPS for selling said information. But the information is already collected by USPS so they can do their job.
You can send a letter to an address without the USPS
a.) Having the address in their database
b.) Knowing who is living there
So Brave, the privacy company, is using a service that collects data about people.