Contrary to popular belief, it would seem that the practice to read Vezos HaBeracha, the final parsha of the Torah, on the second day of Shemini Atzeres wasn't in order to finish the Torah on that day. The gemarra in Megillah 31a simply says that is that day's Torah reading, and it's not clear that they had the custom to finish the Torah then as we do.
Rashi explains why certain festivals had certain readings, but not for the second day of Shemini Atzeres. What is the reason? This answer, addressing a different question, cites two reasons:
- (Sefer Ha-Eshkol, Sefer Ha-Manhig, Abudraham, Orchot Chaim, see references here) include so that the blessings of Moshe, as they appear in the final parasha of the Torah, are purposely read on the day on which we read how Shlomo Ha-Melekh blessed the people of the eighth day of Sukkot (Melakhim I chapter 8)
- because the Torah mentions the commandment of “simcha” twice on Soukot (see Devarim 16:15) (The Machzor Vitry 385)
I'm looking for other reasons (if there are any). If these are the only two reasons given, that can count as an answer.