Leaving home for the sukkah merits Torah

מו"ז ז"ל אמר עפ"י המדרש תנחומא בפסוק והם תכו לרגליך על ת"ח שמכתתין רגליהם מעיר לעיר וממדינה למדינה לשמוע דברי תורה ע"ש.

My grandfather, of blessed memory, said, based on the Midrash Tanchuma on the pasuk "and they sat at Your feet" (Devarim 33:3) — that this refers to the talmidei chachamim who wear out their feet [going] from city to city and from province to province to hear words of Torah; see there.

The Chiddushei HaRim cited the Midrash that reads "tuku l'raglecha" as the Torah scholars who travel from place to place, wearing down their feet in their devotion to hear and learn Torah.

ואמר שלכך אחר סוכות ע"י שיוצאין מבית לסוכה זוכין אח"כ לתורה.

And he said that for this reason, after Sukkos — through leaving one's house for the sukkah — one then merits the Torah.

Just as the scholars' wandering for Torah earns them its light, so the act of leaving one's settled home to dwell in the sukkah is a comparable "journeying" that merits the Torah of Shemini Atzeres / Simchas Torah.

ולכן יש אח"כ שמחת תורה.

And therefore there is afterward Simchas Torah.

This is why Simchas Torah follows Sukkos: the displacement from home to sukkah is rewarded with the joy of Torah.

והראה רמז בתרגום תחות עננך כו' נטלין על מימרך ע"ש.

And he showed a hint in the Targum, "beneath Your cloud... they journey at Your word"; see there.

The Targum's rendering links being "beneath Your cloud" (the sukkah, the Clouds of Glory) with "journeying at Your word" — connecting the sukkah-dwelling to traveling for the sake of Torah.

וי"ל עוד עפ"י זה תכו לרגליך הוא בעליות רגלים שלש פעמים בשנה.

And one may further say, based on this, that "tuku l'raglecha" refers to the pilgrimage festivals [aliyah la'regel], three times a year.

Reading "raglecha" as connected to regel (festival/foot), the verse hints at the three pilgrimage festivals when Bnei Yisrael ascend to the Bais Hamikdash.

וכיון שחג הסוכות רגל האחרון לכך זוכין אח"כ להארת התורה.

And since the festival of Sukkos is the last regel, therefore afterward one merits the illumination of the Torah.

As the final pilgrimage festival of the year, Sukkos culminates the cycle of aliyah la'regel, and this completion brings the light of Torah on Simchas Torah.

ועתה שאין לנו עליות רגלים רק בחג הסוכות היציאה מביתו לסוכה הוא מעין עליות רגלים כנ"ל:

And now that we have no pilgrimage festivals, on the festival of Sukkos alone the going out from one's house to the sukkah is a semblance of the pilgrimage festivals, as above.

In our times, without the Bais Hamikdash and aliyah la'regel, the very act of leaving home to dwell in the sukkah serves as a substitute pilgrimage — and thereby still merits the illumination of Torah.

Summary: Just as the talmidei chachamim wear out their feet traveling to hear Torah, leaving one's home to dwell in the sukkah is itself a kind of journeying that merits the Torah — which is why Simchas Torah follows Sukkos. Reading "tuku l'raglecha" as the pilgrimage festivals, Sukkos is the last regel of the year, and in our times when there is no aliyah la'regel, going out from home to the sukkah serves as a semblance of that pilgrimage, drawing down the illumination of the Torah.