file field formatters: also for images + new formatter 'mime-icon only'

Sometimes you only need 'something' to see if an image/file exists, and you don't bother it's name.
So, a formatter 'mime icon' would be nice. ATM I cannot produce that, not even with 'trim output'.

Also, why are file formatters not exposed tot images fields? (I do understand that image formatters cannot be exposed to file fields)