How did you register the app? If you register it on Azure Portal or using the old portal for app-registrar, we can login the app since the external account also supported by the Azure AD. However, it is not able call the Mail REST.
To make the app compatible with Outlook.com and Office 365 account, we need to register the app using the new portal here. And you can refer to the article for more detail about the new authenticate model. But it seems that the new portal is still in designing and it is not working for the mailbox of Outlook.com at present. I got the error below when I login the app using the Microsoft account:

And for this I issue I have contacted the Office developer team via UserVoice.
Are there any benefits to using an organization-controlled account to hold these application credentials, instead of a random Outlook.com account?
No. Based on my understanding, the benefit for the new portal is that making it easy for the app to support both Office 365 account and Microsoft account. Before we need to register and handle the authentication separately. And if you are interested in the token the app using, you can decode it from here.