Not for records keeping.
Asking the Hard Questions: Email
Nope, you've got it exactly backwards. We should be discussing what the successor of email should look like and designing it such that asymmetric and symmetric encryption schemes can be slotted in and out of the protocol with a minimum of disruption. PQ crypto is already being worked on by a number of reputable groups, including djb's research group. When the algorithms are vetted and the implementations mature, they can be utilized.
It's similar to what's happening with TLS. There was already an experiment using PQ crypto for TLS connections.
imperialviolet.org
Notice that it was an addition of a PQ scheme to TLS, not scrapping TLS and starting over.