Shabbos As Boundless Freedom

וענין חמשין זמנין אידכר יצ"מ באורייתא דאין לך בן חורין אלא העוסק בתורה לכן נמצא נ' דרכים בתורה איך להיות בן חורין מכל שערי טומאה

The matter of why Yetzias Mitzrayim is mentioned fifty times in the Torah is because there is no free man other than one who toils in Torah; therefore there are found fifty pathways within the Torah, each one a way to become a free man liberated from all the gates of tumah.

The Sfas Emes explains that Yetzias Mitzrayim is mentioned fifty times in the Torah because true freedom comes only through Torah, and the Torah contains fifty pathways by which a person frees himself from the fifty gates of tumah.

ואלה השערים נפתחים בנ' שבתות השנה לכן הוא זכר ליצ"מ והוא נחלה בלי מצרים לכן א"צ תפילין בשבת שהתפילין הם לצאת מאלה המצרים בכח ד' פרשיות שבתפילין

And these gates are opened on the fifty Shabbosos of the year; therefore Shabbos is a remembrance of Yetzias Mitzrayim, and it is a nachalah without boundaries (a heritage with no constricting borders) — and for this reason one does not require tefillin on Shabbos, for the tefillin serve to take a person out from these straits and boundaries through the power of the four parshiyos contained in the tefillin.

These fifty gates of holiness open through the fifty Shabbosos of the year, which is why Shabbos commemorates Yetzias Mitzrayim and grants a boundless inheritance; since the work of breaking out of constricting boundaries belongs to the four parshiyos of tefillin, tefillin are not needed on Shabbos.

ושבת הוא גופי' חירותא כנ"ל:

And Shabbos is, in its very essence, freedom itself, as was explained above.

Shabbos by its very nature is freedom, so the liberating work of the tefillin is already accomplished within it.

Summary: The Sfas Emes addresses why Yetzias Mitzrayim is mentioned fifty times throughout the Torah, explaining that genuine freedom is attained only through toiling in Torah, which holds fifty pathways for liberating a person from the fifty gates of tumah. These gates of kedushah open through the fifty Shabbosos of the year, which is why Shabbos is a remembrance of Yetzias Mitzrayim and bestows a nachalah without any constricting boundaries. Because the function of tefillin — through the power of their four parshiyos — is to draw a person out of those straits, tefillin are not required on Shabbos. Shabbos itself is, in its very essence, freedom, so the liberating avodah of the tefillin is already fulfilled within the day.