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

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 Fellowship of the Ring:

• Dumbledore Gandalf sings "The Road Goes Ever On"


• Aragorn sings "Song of Beren and Lúthien" on Weathertop


• The elves sing a "Lament for
  
  

  
  

  Gandalf" in Lothlorien

  
  

In 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.}