I agree with Payments (PCI-DSS hell) & Notifications (especially email & SMS), but Authentication? Fuck no. Unless there is a business requirement for sharing your authN scope with multiple external systems, you should not worry about plugging your app's auth into someone else's idea of a good time. Consuming external authentication providers like Active Directory is something we do today, but it barely registers as "more complex" than integrated user management because its still the same server+process handling everything and all of the authentication state still lives on the same box (AD writes audit logs but these are out of scope from the actual auth flow).
We started trying to plug our app into an external SAML authentication flow (Azure) and it is making it much harder to prove certain semantics around user session lifetime and app security. Maybe it would be "easier" if we had just started with cloud native shiny BS, but I doubt it. Auth state would still be scattered across multiple systems, even if they all lived in Azure (or wherever).
Any time you take a problem that exists on one computer and spread it across many computers, it gets exponentially more difficult and prone to error.