Why don't any characters sing in the 2nd and 3rd Hobbit films?

Question

Tolkien's books have a lot of songs in them, which sometimes become actual songs sung by the characters in the films. The films seems to favor having the characters sing on screen more and more, as the number of songs in each installment seemed to grow as the franchise continued.

In The Fellowship of the Ring:

• Gandalf sings "The Road Goes Ever On"
• Aragorn sings "Song of Beren and Lúthien" on Weathertop
• The elves sing a "Lament for Gandalf" in Lothlórien

In The Return of the King:

• Pippin sings "The Edge of Night" for Denethor
• Arwen sing "Arwen's song" (but that was a deleted scene so maybe it doesn't count)
• Aragorn sings "Elendil's Oath" at the coronation

In The Hobbit: An Unexpected Journey:

• The dwarves sing "Misty Mountains"
• The dwarves sing "Blunt the Knives"
• The goblins sing "Down in Goblin Town"

In the first Hobbit film we hear not one, not two, but three new songs! It therefore seems very strange to me that there is suddenly no singing in Desolation of Smaug and none in Battle of The Five Armies, especially since the song "Misty Mountains" was so popular. Why don't any characters sing in the 2nd and 3rd Hobbit films? Have the filmmakers commented on the lack of songs in the last two Hobbit Films?

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_{NOTE: I'm asking about songs the characters sing (Disney musical style); I'm not asking about end-credits songs, or parts of the musical score that feature vocalists, etc.}

Answer 1

There are songs in the final two Hobbit films.

Bard sings/recites "The Lord of the Silver Fountains" in The Desolation of Smaug:

The Lord of Silver Fountains, the King of Carven Stone, the King Beneath the Mountain, shall come into his own. And the bells shall ring in gladness, at the Mountain King’s return, But all shall fail in sadness, and the Lake will shine and burn.

It should be noted that most of the songs that do appear in the movies are either greatly altered or taken out of context from how Tolkien wrote them. (For example Merry and Pippin's Green Dragon song in FotR:EE takes a couple of lines from A Drinking Song and a couple of lines from The Bath Song.)