Softwords: I am not defending women wearing Tefillin. Ad’raba. However, we must be honest about the Sugya. If Guf Naki means just not expelling gas, then there is little reason to prevent a women from wearing Tefillin on that consideration. And see the Mishnah B’rurah’s comment inside. He is clearly just referring to the fact that (in his time) women were less hygienic than men.
The issue of minimizing wearing Tefillin nowadays is the Derech that Rov Achronim take in the Rama. It’s quite a Pele, honestly, that the Mishnah B’rurah seems to explain the Rama as a hygienic issue. Nowhere does he mention minimizing Tefillin to just Sha’as Tefillah. Presumably this is because he holds that L’chatchilah people should wear Tefillin as long as they can (he makes a few comments that seem to go against the general Mehalach in the Rama, such as that one should wear Tefillin for a Seder of Limud after Davening).
And it is not Chazal who said not to wear it. It is a Shittah developed (well, starting with some references by Tosfos) by the later Ashkenazic Rishonim. The Minhag certainly follows these Rishonim. But it has no mention in Chazal and is not an actual Issur D’rabannan. We have to be honest when learning in explaining these Shittos.
And, by the way, because of this Rama and limiting Tefillin only B’sha’as Tefillah, I have on numerous occasions made it known that I think that someone who misses Shacharis (is sick, sleeps past Chatzos, has some sort of emergency) should only put on Tefillin when Davening Mincha, not at any other point in the day.