We isn't an imprecise word at all, it's very precise in it's definition.

I can honestly not come up with a single example of the distinction between 'zanmen and women' being useful besides this specific case where you really want to be able to say in 1 sentence that you identify as the same group as someone else, but that that group is subdivided into 2 groups, and you're talking about the sub-group that you're specifically not a part of.