Hey Syabab,
Will this affecting all users?
The template override will affect all users. But you can place checking in the code so that the system check for certain profile type ids in order to display those buttons.
Is this a bug? Or ES purposely leave it at profile page?
This is not a bug. It's just that there is no such feature currently. If you would like this feature, feel free to post it in the feature request section.
I think it is not consistent when we can disable it in registration form and edit profile, but it still can be access through Profile Page.
The settings in the workflow is only for the workflow, not the feature itself.