> I guess the equivalent would be if I could ask you to send a PDF to my specific IPv6 address, and you could peer-to-peer shoot it directly to me.

That's not exactly complicated if either party owns a web server. Which - last I checked - the government has.

Just give the person who needs to send the sensitive documents a short link like uploaddocuments.gov, have that page ask for some basic identifying info, and have a box for the user to drag and drop a file. At which point the browser will p2p upload that file over HTTPS.