Daf Yomi - Sukkah 47 - Shmini Atzeres by Rabbi Yosef Dov Karr

The Rosh writes that we do not pronounce a bracha upon entering a sukkah on Shemini Atzeres because doing so would be a demonstration of contradictory behavior. If we are declaring our being in a sukkah as a mitzvah, it cannot be Shemini Atzeres. And if it is Shemini Atzeres, and Sukkos is over, then our entering into a sukkah cannot be a mitzvah. Simply entering a sukkah without reciting a bracha is not inconsistent with it being Shemini Atzeres, because people occasionally eat outdoors if they feel that it is pleasant for them. Our sages did not enact to take lulav on Shemini Atzeres without a bracha, because this is not an activity which people do on their own, and taking it would be an overt sign of our denying that the day is Shemini Atzeres. Tosafos adds that taking lulav would involve handling what may be muktzah on Yom Tov.

Ritva points out that not only can entering a sukkah be interpreted as an elective activity, rather than a violation of Shemini Atzeres, but the fact that we do not recite a bracha is also a demonstration that we are only dwelling in the sukkah due to our uncertainty about the calendar date, and it therefore does not undermine the kedusha of the Yom Tov.

Maybe we can able this to wearing tefillin on Chol HaMoad According to the Rosh we should not wear Tefillin because it would be a demonstration of contradictory behavior of the nature of Chol HaMoed, is it chol or Moed? If its Moad then we never wear Tefillin. According to the Ritva, however we should wear Tefillin without a bracha due to the uncertainty about the date. .Clearly the two opinions have nothing to do whether or not one works of Chol HaMoad or not.