AFAIK no one is transitioning to PQC algorithms by abandoning classical ones. They concatenate classical and PQC - so-called hybrid.
To your point about PQC being used exclusively, post-quantum encryption methods are designed to be resistant to both quantum and classical attacks. That is one of the key stated goals of the NIST post-quantum cryptography program.
The McEliece cryptosystem[1] is one of finalists in the PQC competition and it's also quite old - developed in 1978. It didn't face as much scrutiny as RSA or ECC due to its large key sizes which resulted in nonexistent adoption.
My understanding is that all the other PQC candidates including Kyber are much newer and far less studied.