I've looked at Cognito in depth, and it seems like an abandoned service. Hundreds of open issues that got rolled into the Amplify issue tracker, with little to no response. It lacks some pretty basic SAML capabilities, like IdP-initiated logins. If your customers want to put you as an icon in their Okta dashboard or whatever, can't do it. They reported that as being "on their roadmap" in 2017.
It does work for the basic use cases, so I would still consider that an better option than rolling your own for the average service provider.