It's possible that the TPM spec will be updated to allow for loading pre-encrypted data into the TPM store as a response to this. Alternatively, existing secure computing systems (SGX/TrustZone) can also be used to decrypt the synchronised key relatively securely.
instead they wrap/seal everything instead with a layer of crypto, then you can pass that wrapped object around as much as you want, only the TPM can unseal it
a TPM could easily be instructed to seal an internally generated secret with additional escrow keys for MS/Apple/...
that plus remote attestation could make it so you can never see the key in the clear
The problem is that you need private/public key pairs that are synchronised across devices for FIDO to work properly cross-device. When you register an account on your phone, you need that account key on your desktop to use it there, and that's nearly impossible without some kind of key sharing mechanism.
Funnily enough, a system for signing web authentication requests from a mobile device is far from new: I've been using https://krypt.co/ for years (though it's on the long road of sunsetting right now) and I hope that will last long enough for the new cross device standard to replace it.