View All Data is not, in fact, View All Data.
If I grant you View All Data permission in Salesforce, you can indeed view all data, if field level security allows you to see the field first. So if you don't have permission to My_Object__c.My_Field__c, that field doesn't exist, even if you can View All Data.
The below script will go over a set of objects and grant read permission at the object and field levels. It is super ugly, but it works, and beats going through seven thousand slow-as-**** screens to add each field individually.