A lot of the argument here is misunderstanding.
According to R’Moshe the purpose of the mechitza is to avoid kalas rosh (mingling, improper conversation, etc.). A balcony obviously avoids the problem because there can be no interactions between the genders.
Kalas rosh (certainly during prayer) is an issur d’oraisa. If the people could be trusted to not engage in kalas rosh, then no mechitza would be necessary. During the second Bais Hamikdosh it was noted that there were incidences of kalas rosh during Yom Tov in the Bais Hamikdosh. They therefore instituted a balcony during those times.
In other words the institution of a mechitza is d’rabbanan but the problem it is meant to prevent is d’oraisa (a fairly common occurrence). If one is confident that there will be no kalas rosh then the only problem davening in a shul without a mechitza is d’rabbanan.