The prohibition against getting married on Shabbos is rabbinic in origin. It was part of the gezeirah against mekach u'memkar (buying and selling) shemo yichtov (lest one write by mistake). However the prohibition against marrying on yom tov or even on chol hamoed is Biblical based on the principle of ein mearvin simcha besimcha. On yom tov, and even on chol hamoed, there is a mitzvah to rejoice, and one who marries is engaged in a different form of simcha, which detracts from the simcha of Yom Tov. (On Shabbos there is no mitzvah of simcha, hence no problem of contradiction.)
In Talmudic times there were several differences between the practices of the Jewish community in Babylonia and the practices of the communities in Eretz Yisrael. One of these differences was regarding krias haTorah. In Babylonia they would complete the reading of the entire Torah every year on the last day of Sukkos, hence the name Simchas Torah. In Eretz Yisrael each sedra (read each Shabbos) was only about one third the length of the sedros read in Babylonia, hence it would take about three years to complete the entire Torah. Simchas Torah would only be celebrated once every three years, upon the completion of the entire Torah. Already in the times of the Rambam the practice all over the world had followed that of Bavel, to celebrate Simchas Torah every year, on the last day of Sukkos.
The Achronim raise a problem regarding this practice: why is this celebration not in violation of the principle of ein mearvim simcha besimcha? On Sukkos there is clearly a mitzvah of simcha, and the celebration of the siyum of the Torah also certainly involves an element of simcha. Why should we not insist on observing Simchas Torah only on a Shabbos or a weekday, as opposed to having the celebration on a yom tov?
Perhaps the answer to that question lies in the nature of the yom tov of Shemini Atseres. Each of the yomim tovim has its own theme. The theme of Pesach is the redemption from Egypt, on Shavuos it is Mattan Torah and the theme on Sukkos is the ability of the Jewish people to have survived miraculously throughout the years of the galus. For seven days we leave our permanent home and dwell in the shaky sukkah, with very little protection. We rely on the Divine protection, which has maintained the Jewish people throughout the years, despite all odds against survival. In the language of Rav Kook zt"l, the continued existence of the Jewish people is a, "halacha leMoshe miSinai" (i.e., there is no rational way to explain it).
What is the theme of Shemini Atseres? The halacha declares Shemini Atseres as a separate yom tov, and is not merely the last two days of Sukkos. (This is the reason that the brocho "shehechiyanu" is recited at the end of the Kiddush on the evening of Shemini Atseres but not on the evening of the last days of Pesach. Shemini Atseres is a separate Yom Tov, and has not been celebrated since a year ago). What is the special theme of the new Yom Tov?
Rashi, in his commentary on the Torah (Vayikra 23:36), quotes from the tanaim that after the seven days of Sukkos are all over, and the millions of Jews have spent their yom tov in Jerusalem (fulfilling aliya laregel), HaKadosh Baruch Hu exclaims, "I love you so much; I find it difficult to say goodbye; please stay on another day". Shemini Atseres does not come to commemorate any particular historical event, but rather to emphasize bechiras Yisrael, the uniqueness of Am Yisrael. From all the nations of the world, the Jews alone were chosen to be designated as "bonim lamakom", as "bni bechori Yisroel".
The entire uniqueness of the Jewish people lies in the fact that the malach (angel) teaches every baby the entire Torah before he or she is born. The simcha of the completion of the entire Torah is not something separate from the simcha of the yom tov. The whole essence of the yom tov of Shemini Atseres is interconnected with Torah study. Only through Torah study did we become the Am Hanivchar, and hence our minhag of celebrating the simcha of completing the learning of the entire Torah not only does not compete with the simcha of the yom tov of Shemini Atseres, it rather complements it and enhances it.