What does a relying party that combines its own IdP with external IdPs look like in practice?

A typical login page such as Doodle's offers both: create or use a local account (the RP's own integrated IdP) or continue with Google, Apple or Facebook (external IdPs), so the same service is isolated for some users and RP-centred federated for others.

This hybrid is the most common shape on the consumer web. The service keeps a local user management for people who do not want a social login, and at the same time accepts several external identity providers for those who do. From the user's perspective it is a choice between convenience (one click, but the platform learns about the visit) and independence (another password, but no third party involved).

For the RP the hybrid adds up the costs of both models: it still runs its own identity processes for local accounts and maintains the external integrations. It accepts that cost because it enlarges the audience and lowers the sign-up barrier.