The gemora 5: omud merubeh al haporutz by a movue is a kal vochomer from chotzer the question is why do I need to learn from chotzer, by all the dinim in the Torah you have omud merubeh al haporutz (example asleh in the gemora later)?
We only have a source in the Mishnah for the principle of Omed Merubah Al ha'Parutz in the laws of Kila'yim, Tum'as Ohel, and Reshus ha'Yachid. How do we know that the principle of Omed Merubah Al ha'Parutz applies to a Mavoy? We have to learn it through a Limud (such as a Kol v'Chomer) from one of the places where we know that it exists. The Gemara chose to learn the principle from Chatzer because it is most similar to Mavoy.
In addition, perhaps it could be that mid'Oraisa, we know that Omed Merubah applies to a Mavoy as it does to all laws regarding Mechitzos, as you wrote, and as long as a Mavoy is Omed Merubah Al ha'Parutz, mid'Oraisa it is a Reshus ha'Yachid and not Reshus ha'Rabim. However, perhaps the Rabanan did not permit carrying in a Mavoy which is Omed Merubah, but only in a Mavoy that is completely enclosed. Since the Rabanan prohibited carrying in a Mavoy (even though mid'Oraisa it is not a Reshus ha'Rabim) and required making a Lechi or Korah, so, too, they could have required that the fourth wall have either a Lechi or be fully intact and not Omed Merubah. The Gemara therefore teaches a Limud from Chatzer, where we find that Omed Merubah does work and the Rabanan did not prohibit carrying in a Chatzer that is Omed Merubah.