This had me curious, so I tried googling for

  site: *.gov fax

Was surprised at the results. It may not be the only conduit, but it is there for job applications, VA benefits, applying for a headstone in a national cemetery, court filings, IRS documents, and much more.

The FBI recently stopped accepting FOIA requests online and now online accept them via fax and snail mail.

They did it deliberately to reduce the number of requests.