Actually, Facebook was in fact a relying party for a time. See https://www.wired.com/2009/05/facebook-opens-up-to-openid/ https://www.wired.com/2009/05/facebook

Actually, Facebook was in fact a relying party for a time. See https://www.wired.com/2009/05/facebook-opens-up-to-openid/ https://www.wired.com/2009/05/facebook-opens-up-to-openid/ for example. Adoption was negligible so they eventually killed it.