You don’t need that if you include quote in CSR and then CA validates the quote and writes the validation result in the certificate. Certificate then contains proof that private key is in TPM.
That said, TPM quotes are attesting the value of TPM PCRs which are just registers of hashes (representing the state of the machine).
When making a CSR, you can use https://tpm2-tools.readthedocs.io/en/latest/man/tpm2_certify... to attest a key is TPM-resident.
I think your central thesis is that at the time of TLS establishment, why not use PKCS11 (with a cert signed by a CA that has validated a TPM certification), and I agree: services should probably integrate via PKCS11.
Sorry to have missed that!