There is a single search parameter defined on Binary: contenttype.

It seems impractical to search for binary resources of a particular mimeType. "Give me all the binaries you have of application/pdf" will result in a huge response. Granted it will be smaller than "give me all the binaries you have" but still not useful. I'm not sure there is any meaningful search parameter on Binary as it stands now. Is there a use case for this search parameter?

On the other hand, the supposed benefit of Binary is its dual personality: sometimes its a FHIR resource, and sometimes its a blob. However, in a search result, you'll only get back the resource "personality". This is an inefficient representation fo rthe contained content, and makes a search result particularly unwieldly. This is a case where a search result of only the references would be helpful: (a) to be able to control the size of the response, and (b) to be able to retrieve the content directly as their native representations.