When to add a field to an asset?
It makes sense, when it's a task that should only be done once and is directly related to the asset.

A good example I have of an Asset custom field is a field allowing the content-administrator to define where an images focal point is positioned e.g. top left, bottom right, top right, etc.

I'm able to make use of the field EVERY time I display the image asset, but only need to deal with the custom field, once.



Part deux (in answer to your comment): 

Yes, in my experience, although you can also double click an asset from the new/edit entry screen and see it's custom fields e.g. "Focal point position". See image below...