@andrei_chiffa @dangoodin the issue is the size of the handshake itself. You have to run the entire handshake before you can transmit data. With PQC, what used to be a 32 to 256 byte public key or signature now each becomes 1 to 3.5 KB in size. This is acceptable for the key agreement parts, since we really only need one artifact per party there, but becomes way too expensive when talking about the certificate, i.e. a chain of public keys signed by keys further up.
Merkle Tree Certificates are a proposal that significantly compresses this certificate chain, at the cost of a more complicated trust management story.