I've never wanted to completely hand over authentication to a third-party.

Instead what I'd think I'd like is just the risk assessment to be be performed by a third-party when I'm handling authentication (i.e. a third-party that has a broader view of what's happening across multiple services over time). I just send the pieces of information that I'm willing to share as an API call and they make the best risk assessment they can.

Then I can take that risk assessment result and make a final decision if authentication succeeds or not.