The Miracle Gap: Pesach Without Krias Yam Suf

The Torah doesn't provide a date for the splitting of the sea. 

Chazal (e.g., Seder Olam Rabbah 5), however, place krias yam suf on the last day of Pesach (cited by Rashi to Shemos 14:5). 

Seforno (Vayikrah 23:36, Devarim 16:8) sees the song that Israel engaged in together in praise of HaShem for that event as what imbued shevii shel pesach with the status of a Yom Tov. 

People tend to view Pesach as getting started with the Exodus on the 15th (the catalyst for the first day being a YT) and culminating seven days later with krias yam suf, when the Egyptians were fully removed from the picture, thus completing Israel's salvation from the Egyptians. 

However, in Rambam's telling, Pesach seems to be exclusively a celebration of the miracles that happened in Egypt and the Exodus, but nothing thereafter, significantly altering Pesach's character.

In MT (Chametz uMatzah, 7:1-2), Rambam is clear that the mitzvah of retelling the Exodus account is limited to the miracles that occurred in Egypt, seemingly excluding the desert miracles. 

In the Haggadah included in MT there is no mention of krias yam suf (Hallel aside). *

This is made clear in MN (3:43) where Rambam writes that Pesach is to commemorate the miracles that took place in Egypt whereas Sukkos is for remembering the desert ones. 

While it is true that the Torah only and always mentions the miracles that occurred in Egypt and the Exodus in association with Pesach, however, insofar as Rambam presumably accepts the Rabbinic dating of krias yam suf, what is the qualitative difference between the Egypt miracles and the desert ones that leads Rambam to exclude the latter from the Passover rites?

I believe that chapter 8 of Yesodei haTorah holds the key to the answer. 

Rambam writes there that all the miracles that occurred in the desert—krias yam suf included—were only performed due to contingent want. 

Had there been no need to provide Israel with food, drink, protection, or to put down Korach's rebellion, the desert miracles would not have occurred. In other words, they were solely miracles of utility.

The miracles that occurred in Egypt, on the other hand, were necessary and indispensable for introducing world-changing ideas to mankind.

The Egypt miracles, culminating with Mattan Torah, were wrought with the intention of showing God's knowledge and control of this world as well as establishing Moshe as His prophet par excellence (Rambam ad loc. and Ramban to Shemos 13:16). 

Pesach, for Rambam, is about commemorating miracles whose purpose was to shape Israel's emunah and theology—which were limited to those that took place in Egypt. 

In contradistinction, Sukkos is about celebrating the miracles that were necessary for meeting our ongoing physical and spiritual needs as they arose—those that took place in the desert. 

(See Hararei Kedem, volume 2, topic 81, where the significance of krias yam suf in relation to the Exodus [which is evident from the second chapter of b. berachos] is connected to the mitzvah of the daily remembrance of the Exodus [as opposed to the annual mitzvah of sippur—which is limited to the night of the 15th of Nissan], which in turn in subsumed under the daily mitzvah of krias Shema and is noteworthy for the elevated level of kabalas ol malchus shamayim it generated.)

* It's been brought to my attention that Rambam's son R. Avraham testified that Rambam actually did say those omitted sections at his own Seder, see here.