Yea, e. g. if you lower treble frequencies most likely the soundstage will get smaller, details are also harder to pick out of the mix if the treble is on a lower volume. Imaging is also kind of dependent on treble frequencies in my experience. Tactility is probably one of the things that I haven't noticed changing too much, because it is more of a "technical ability" of the driver itself.

However, most headphones tonalities benefit massively from EQ, so I am not too concerned about the negatives. Some headphones shouldn't be EQ'd too much though in my opinion, e. g. the HD800 and HD800S lose much of their "speciality" (their massive soundstage and fantastic imaging) if you lower the treble volume too much.