From my singing days in school choirs, our choir teachers always made a big point of standing to sing, versus sitting.
You can't get near the volume when you sing sitting versus when you sing standing.
My guess is a 4" heel creates enough unsteadiness in balance (especially if the woman isn't used to them) that vocal performance will be slightly affected.
That being said, if you got a bad voice, you will still sound awful while barefoot while someone with a well-trained nice singing voice, will sound good no matter what shoe they are wearing!!