Eiruvin 96a - Women in Non Time-bound Mitzvos

The gemara tries to prove from the fact that Michal bas Shaul would wear tefillin that tefillin must me a mitzvah that is not bound by time, therefore women would be obligated. That would explain why the Rabbonon allowed her to wear tefillin and didn't protest. But, if tefillin was a time-bound mitzvah, the gemara assumes that chazal should have protested against Michal wearing tefillin.

Two things need to be explained in this assumption. The first is something that both Rashi and Tosafos struggle with. Why does the gemara assume that if it were a time bound mitzvah, chazal would protest against women wearing tefillin? Secondly, why does the gemara assume that if it were not a time bound mitzvah, everything makes sense. If it were not a time bound mitzvah, everyone would be obligated to wear tefillin, not just michal!

Regarding the first issue, Rashi writes that for women to do mitzvos that they are not obligated in is a violation of bal tosif. Rashi seems to mean that it is a d'rabonon violation of seeming like a bal tosif. However, to avoid Tosafos question as to how we find Hilni sitting in a Succah, the Gaon Yaakov explains that perhaps it is only a problem of bal tosif by mitzvos that are obviously being done only for the sake of the mitzvah, to the exclusion of succah which is not as recognizable that she's was doing it for the sake of the mitzvah (rather for the sake of being mechaneich her children to sit in a succah). Tosafos has another approach. Normally we encourage women to perform time bound mitzvos and according to Rabbeinu Tam even allow them to make a bracha on it. However, by the mitzvos that are particularly mentioned in our gemara - Tefillin, aliya l'regel, semicha and blowing shofar, there is a "risk" by each of them of some violation which causes chazal to discourage one who is not obligated from doing these mitzvos. By tefillin there is a risk of not maintaining a sufficiently clean body, by aliya l'regel there is an impression of bringing chulin l'azara, by semicha it is tantamount to avoda b'kodshim, and blowing shofar is an issur d'rabonon. 

The second issue is addressed by the Gaon Yaakov. Why does the gemara assume that if it were not a time bound mitzvah, everything makes sense. If it weren't a time bound mitzvah then all women would need to wear tefillin, not just michal? The Gaon Yaakov explains that Chazal understood that even if women were technically obligated in tefillin, Chazal were gozer on them not to wear tefillin due to the difficulty of maintaining a clean body. However, if m'doraysa women were obligated, it would make sense that some outstanding women such as Michal would make an effort to do it and it would not be discouraged by chazal. This seems to be the gemara's assumption. But, this still requires some more explanation. If women and men would be equally obligated in the mitzvah of tefillin, why would chazal exempt women from this mitzvah but mandate men to perform this mitzvah? Is their assumption that biologically it is somehow easier for men to maintain a clean body than it is for women or perhaps they felt that men would take it more seriously than women? Either way it doesn't seem that there would be a halachic difference between men and women, it would only be a practical difference.