So it's the Touhou effect: without their unique head gear, they lose their identity?

Well... without the side ponytail, Akagi and Kaga can also look quite similar.
Especially Akagi since she's rather generic in appearance

Well, it's monochrome, and there are a lot of characters that have dark brown or black hair, they generally only have 2-3 body types to choose from, and different artists frequently change bust or body shapes to suit personal tastes, anyway, they don't have their usual clothes, or gear, and facial features change too much from artist to artist to really be distinctive unless they had something really obvious like a mole or something, and they don't.

So basically, yes, hats and funny hair styles are generally there to keep different artists from making characters from a series with loads and loads of characters who are all slim teenaged girls distinquishable.