I wouldn't say that because, aside from Generations, we never see the crews of the Enterprise D, Voyager, or DS9 switch back and forth between the 2 designs. The Enterprise crew always wore their style of uniforms, Voyager there's, and DS9 started out with Voyager style uniforms but later moved to 1st Contact style uniforms. So this suggests to me that they're all completely different uniforms and not different classes of uniform.
As for the Lower Decks style uniform, that's unique to the Cerritos or at least the crews of Cali class ships. When they showed Riker and the Titan, everybody there were wearing the First Contact style uniforms and when Boimler later transferred to the Titan he wore the same style of uniform as the rest of the crew aboard the Titan. So the LD style uniform is not standard issue and did not replace the 1st Contact style uniforms. At best, they're a new uniform that they're looking to make standard and are currently field testing them on Cali class ships.
Regardless, my point still stands. People in Trek and other sci-fi franchises are still running around in the equivalent of service dress uniforms instead of something more comfortable and practical like the blue coveralls that the US Navy has started to issue for standard wear aboard ships for both enlisted and officers. Before that, officers and Chiefs wore khakis that didn't seem too uncomfortable, although not as practical as the coveralls are. And if we go back to the age of sail, yes, officers wore what would be the equivalent of dress uniforms now a days, but not the enlisted personnel who did all of the work. Officers could get away with the uniforms they wore because they wouldn't be doing any of the work, they'd just stand around and supervise. On the ground that's a different matter, but linear warfare was different than modern warfare and troops back then didn't regularly run around diving for cover. Besides, by the late 19th century simpler, less elaborate uniforms were coming into being, at least for enlisted personnel with drab colored uniforms starting to come into being by the early 30th century.