I am having the same issue as Skaldhor above.
The exchange online role permissions have been setup to only allow Get-Mailbox as the cmdlet and when i attempted to run Connect-ExchangeOnline with certificate information i get "The role assigned to application <GUID here> isn't supported in this scenario. Please check online documentation for assigning correct Directory Roles to Azure AD Application for EXO App-Only Authentication.".
When i assign the app registration the Exchange administrator role in Azure AD the Connect-ExchangeOnline cmdlet works but i can use all of the exchange cmdlets as if the app registration has full permissions over the exchange tenant.
Can we please get some more clarification here?