[tialaramex]

Yes, if this ever works and is affordable.

Suppose our adversaries have a machine which can do Shor's algorithm at the scale needed to break modern public keys for say $1M and an hour, and they have been recording encrypted sessions.

For sessions encrypted using RSA key exchange, it is enough for them to spend $1M and wait one hour and then they can decrypt everything that they've recorded, using one particular key. So e.g. a typical HTTPS site only has one key for months or even years, if they've recorded the encrypted data they can read all of it for $1M.

Where Forward Secrecy (e.g. ECDHE) was used, the cost is $1M (and an hour) for each session, because the keys change each time so each fresh session needs the expensive algorithm.