The following is based on R' Samson Raphael Hirsch's commentary on these verses.
Let's work backward from the ultimate purpose of this special reading, which the Torah is kind enough to tell us (v. 6):
הַקְהֵ֣ל אֶת־הָעָ֗ם הָֽאֲנָשִׁ֤ים וְהַנָּשִׁים֙ וְהַטַּ֔ף וְגֵרְךָ֖ אֲשֶׁ֣ר בִּשְׁעָרֶ֑יךָ לְמַ֨עַן יִשְׁמְע֜וּ וּלְמַ֣עַן יִלְמְד֗וּ וְיָֽרְאוּ֙ אֶת־יְהוָ֣ה אֱלֹֽהֵיכֶ֔ם וְשָֽׁמְר֣וּ לַעֲשׂ֔וֹת אֶת־כָּל־דִּבְרֵ֖י הַתּוֹרָ֥ה הַזֹּֽאת׃
Gather the people—men, women, children, and the strangers in your communities—that they may hear and so learn to revere the LORD your God and to observe faithfully every word of this Teaching.
Gathering brings us to hear the reading, which inspires us to keep up our learning at home and to infuse the fear of God into everything we do, so that we end up knowing how to and caring to apply the Torah's commands to everything we do.
It all, ultimately, leads to the application. And when do we fully apply the Torah? When we're working in the world, particularly in the part of the world we're meant to keep the Torah in, primarily - the Land of Israel.
And when do we work in (and on!) the Land of Israel? For six years out of every seven, starting after the end of the Shemita year. The moment when the Israelite national agricultural economy is about to kick back into gear is the moment when the Israelite nation needs to rededicate itself, as a unit, to learning and following the Torah.
Side note: R' Hirsch also points out that the timing of this observance on Sukkot enhances the same theme: Just as we're about to start doing agriculture and business again, we're also recalling the time "when it was not agriculture or business, but where the miraculous grace of God provided for everybody ..." When we dedicate ourselves to applying the Torah to the coming period of economic activity, it helps to already be in the frame of mind (and of Sukka!) that the real source of our well-being and safety is not the economy, but the Almighty.