I have several disagreements with his approach:
First, the text clearly states that Moshe did not write in prose. It says, "Then Moses and the Israelites sang this song to the LORD."
Second, Miriam *sang* with the women. The text says: "Miriam sang to them: "Sing to the LORD, for he is highly exalted. The horse and its rider he has hurled into the sea." Thus, to propose that they had different responses appears unsupported. Miriam may have incorporated dance, but their initial reaction was the same, which was to sing.
Third, the Song of the Sea is not prose. It's not a literal recounting of the events at the sea. We're told the Pharaoh and his captains sank in the depths of the sea (Verses 4 and 5) but that's about as close as it comes to describing the events of Exodus 14. There's nothing in the song about a splitting sea, or the Israelites walking across on dry land, or indeed about any miracle at all. Moreover, it **differs** from the narrative in the preceding chapter in several ways. As James Kugel mentions, citing research by Frank Cross and David Freedman, the song could be about an event that took place far offshore or, as verse 8 states, "at the heart of the sea" where God's blast of wind from His nose caused a wave to capsize the boats or barges, resulting in the Egyptians sinking "like a stone" and "like lead in the mighty waters". Kugel also points out that "if the Egyptians were pursuing the Israelites on a dry path in the midst of the waters, then there was no place for them to go down or sink, as they were already on the bottom of the sea bed."
Fourth, the conclusion of major sections of the Torah are often marked by lengthy poems. The patriarch tales end with Jacob's Blessings, the Wilderness tales end with Haazinu, and significant periods of David's life also end with poems. The same is true for the Exodus tales, with the Song of the Sea serving as the poem.
Fifth: The Song of the Sea exhibits several traits of poetry, such as the use of metaphor, phonetically overlapping verbs, and a distinct rhythm, which conforms to the conventions of Biblical poetry. It also contains several striking puns, such as the one in the second verse עָזִּי וְזִמְרָת יָהּ, וַיְהִי-לִי לִישׁוּעָה; זֶה אֵלִי וְאַנְוֵהוּ, אֱלֹהֵי אָבִי וַאֲרֹמְמֶנְהוּ. The sense of the word "zimrah" is likely "power" but it puns on the more common meaning of the word "song" With this pun, the poet is saying God is the source of the speaker's power and also the source of the song.
Sixth: In the Torah, the Song of the Sea is structured in a brick pattern, a layout that is used in only one other place in the first five books of the Torah: The Song of Haazinu.