Using X25519Kyber768 adds over a kilobyte of extra data to the TLS ClientHello message due to the addition of the Kyber-encapsulated key material. Our earlier experiments with CECPQ2 demonstrated that the vast majority of TLS implementations are compatible with this size increase; however, in certain limited cases, TLS middleboxes failed due to improperly hardcoded restrictions on message size.
Khyber1024 adds an additional ~400 bytes to the key size, making it greater than 1500 bytes (1568). This will be even more problematic than khyber768.
Except that according to the fine article:
Everyone assumes fines are an incentive to return borrowed materials, but the data show no difference in return rates between libraries that charge fines and those that don't, says DePriest, who wrote a seminal white paper on the topic in 2016.
"The following is not for the weak of heart or Fundamentalists." -- Dave Barry