Other things are external to the EXIF but could be combined with it. The sequence numbers in the filenames are the most obvious signal. The precise number of megapixels of the image might also tell you what sensor was used -- so maybe an anonymizer should resample the image to a new size.
I guess these seem unlikely to be investigated, but then again nobody initially thought that telling every web server what fonts you have installed on your machine would be used against you, or that the existence of "Do Not Track" would make browsers easier to track. It just depends on how much it's worth to someone to write this stuff once -- then it's free for all future uses.
I just looked at https://en.wikipedia.org/wiki/Exif and there are lots of interesting possibilities.
http://www.ws.binghamton.edu/fridrich/Research/double.pdf
http://www.ws.binghamton.edu/fridrich/Research/EI7254-18.pdf
If you're worried about attracting that kind of attention, use a burner device.(source: me examining as many different iPhone models and instances to build deduping heuristics for PhotoStructure)