The thing is that you have modified the UI page template - it is the same template as for the pages. If you have multiple documents using the same page template and you e.g. remove a web part from the template, this change affects all the documents using the template. So, the same happened in your case - this UI page template is also used by the default modules and applications and you have removed the UI web parts from it.
You need to save the template as a new one or as Ad-hoc template and then you can do changes to it.