Many people think about eating in the Sukkah as the main mitzvah, probably because the minhag (as Shulchan Aruch notes in Orach Chaim 639:8) is to only make the Bracha when eating. This is based on the position of Rabbenu Tam who claims that the “primary dwelling is eating”, which seems to be is meant to be a comment about berachot rather than the nature of living in the Sukkah. Nevertheless, some people think that eating is the central mitzvah. However, the simplest understanding of the Gemara is that the mitzvah is not to do a series of actions in the sukkah, but rather to live in the took – teshvu k’ein taduru. As such, eating is just one part of living. The Rambam rules that one makes a bracha every time one enters the sukkah, making it clear that eating has no special status, even on the level of brachot (leaving the first night aside).
However, it should be noted that the Leket Yosher citing the Terumat HaDeshen claims that the primary mitzvah is sleeping in the sukkah. For this reason he claims that one cannot sleep in the sukkah on Erev Chag so that people will sleep l’teavon – desire to sleep (as if a nap has ever made me want to go to sleep less on a Yom Tov…). This is both novel because it puts sleep front and center, and because of the obligation to desire to live in the sukkah, parallel to the one does not eat matzah erev Pesach so that he will desire matzah. These points are highlighted and developed by R. Menachem Kasher in Divrei Menachem 4:24 (here). The previous responsum deals with what else is prohibited on Erev Chag (or why things are not prohibited according to most poskim).
Yes, there are many halachic suggestions as to why most people, at least in Chutz LaAretz don’t sleep in the sukkah, but the simplest understanding of the Gemara is that one must, and, as the Leket Yosher notes, it may be even more important than eating. (This provides an interesting explanation for why the Gemara says one can snack but not nap out of the sukkah, even though both acts are arai – though the Gemara provides another reason.)
Anyways – just some pre-Chag thoughts. Chag Sameach!