The password prompt during Secure Enclave PSSO registration is intentional by design — it's Apple's mechanism to verify the user's identity before binding the Secure Enclave key to their account. It's a one-time enrollment cost, not an ongoing authentication event.
That said, there are two ways to reduce friction:
First — pre-stage the registration silently via MDM before the user's first login. If you push the PSSO extension configuration via com.apple.extensiblesso payload with RegistrationToken pre-populated from your IdP, the password dialog can be pre-satisfied using SSO credentials the MDM already has. Check whether your IdP supports registration token pre-provisioning in their MDM integration.
Second — if you're on Entra ID, the Microsoft Enterprise SSO plugin handles the Secure Enclave binding silently for Entra-joined devices when Company Portal is installed and the device is already registered. The password step is bypassed because Company Portal already holds the device registration credential.
The password prompt being suppressed entirely without one of these flows isn't currently possible — it's a security boundary Apple has intentionally kept.
— Divya Ravi, Senior iOS Engineer