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The general view today is that of course post-quantum cryptography should be an extra layer on top of well-established pre-quantum cryptography. As the French government cybersecurity agency (Agence nationale de la sécurité des systèmes d'information, ANSSI) put it at the end of 2021:
Acknowledging the immaturity of PQC is important: ANSSI will not endorse any direct drop-in replacement of currently used algorithms in the short/medium term. However, this immaturity should not serve as an argument for postponing the first deployments. ANSSI encourages all industries to progress towards an initiation of a gradual overlap transition in order to progressively increase trust on the post-quantum algorithms and their implementations while ensuring no security regression as far as classical (pre-quantum) security is concerned. ...
Given that most post-quantum algorithms involve message sizes much larger than the current pre-quantum schemes, the extra performance cost of an hybrid scheme remains low in comparison with the cost of the underlying post-quantum scheme. ANSSI believes that this is a reasonable price to pay for guaranteeing an additional pre-quantum security at least equivalent to the one provided by current pre-quantum standardized algorithms.
But NSA has a different position: it says that it "does not expect to approve" hybrids. Publicly, NSA justifies this by
- pointing to a fringe case where a careless effort to add an extra security layer damaged security, and
- expressing "confidence in the NIST PQC process".
Does that mean the original NISTPQC process, or the current NISTPQC process in which NIST, evidently surprised by attacks, announced plans to call for new submissions?
Of course, if NSA/IDA have secretly developed an attack that works for a particular type of post-quantum cryptosystem, then it makes sense that they'd want people to start using that type of cryptosystem and turn off the existing pre-quantum cryptosystem.