Earlier quoted context omitted.
Cryptographically speaking it's signing a challenge, not encrypting a value (which would be a public key operation), but generally speaking yes, that's the idea of it! One of the things FIDO adds beyond a protocol for "plain" hardware-generated and stored keys is the idea of attestation, i.e. authenticators being able to express statements like "keys can never leave this authenticator" or "this key requires PIN or fi…
However, you should not require attestation for public services. If you let Jim sign up with his dog's name as a password, but then refuse to let Sarah sign in because her FIDO device wouldn't provide "attestation" you're crazy. Attestation probably isn't the correct choice for almost anybody, but the cases where it could at least make sense are if you're an employer checking employee authenticators, if you gave ever…
But for sensitive systems/services, why not make use of the advanced capabilities that hardware authenticators offer? I'm using one in a corporate environment, and in my view it makes a lot of sense.
I'd also not be upset if my bank would let me bypass the mandatory "account restricted, call customer support" dance every time I initiate a transfer over $10 between my own accounts using only a "trusted" authenticator brand... And banks typically care a lot about security properties like "this authenticator does not allow extracting private keys".