1. Mary Poppins should've sung R. Kelly's "I Believe I Can Fly...I Believe I Can Touch the Sky."
2. Tevye should've sung "Up on the Roof" by James Taylor
3. Henry Fonda & Lucille Ball in "Yours, Mine & Ours" should've sung "We Are Family" by Sister Sledge
4. Phileas Fogg in "Around the World in Eighty Days" should've sung "Up, Up & Away" (in My Beautiful Balloon) by the Fifth Dimension
Okay, I've run out of ideas here, this late at night/this early in the morning.
I'm guessing you've caught my drift here; maybe you have some suggestions for "Songs They Should've Sung"...