What you describe does exist, but not via the post office. For example when I started a new job I had to go to a tiny store that does fax, copy, postal, notary and similar services and have them physically verify my employment eligibility documents. Several similar providers exist all over the city (including FedEx, UPS, banks and more).

This is such a high barrier to entry, however, that people will simply not do it for something that isn't absolutely critical. Online services compete with each other to be as frictionless as possible, whereas this is the exact opposite of that.