You've imagined a whole scenario in your head where the deep space nine style uniform was exclusively associated with space stations despite not only evidence to the contrary at the time, but also knowledge we now have that they get used on several starships later on. Based on what?
Based on the fact that they were referred to as such in the Star Trek Encyclopedia, which was written by members of the show's production staff.
Look, if you don't think the DS9 uniforms were originally meant to be station uniforms, that's your outlook. But there's more evidence than not (to me anyway) that that's what they were supposed to be.