I built my latest application using Amazon Cognito for user management. My application and database don't ever know anything about the passwords. Amazon's problem.
You have two choices: try and do it on your own, or delegate to someone who you think can do it better. There are risks either way. Considering how much data Amazon has, they probably invest significantly more than you (or OneLogin) on security.
While letting them handle the security options is probably going to result in a more secure system for you, it's certainly not "Amazon's Problem" when your database gets leaked and your user data gets out. For example, you're still going to have to explain to your users that you were compromised, and you're still going to show up in the haveibeenpwned list, not "An AWS Cognito Account".