How to use content type tokens File path in file and image field?
One way to do it, is to use File (Field) Paths, as node provides content type "subtokens" like:

[node:content-type:machine-name]


Problem with any other implementation will be caused by the fact that fields can be attached to things that does not have content types.

This answer is limited to nodes, so it's only a partial one, but it will do the trick in many cases.