The film operates by its own quasi-realistic rules, i.e. that this singing woman brings song (back) into a house devoid of it. The music we get, once "Confidence" is out of the way, is mostly diegetic, resulting from Maria picking up a guitar. If these two non singers began to sing, it would suggest Maria's influence has turned the household into .. well, a B'way musical, which the film doesn't want to be. It's a logical decision.
For the record, I saw Parker in the national of "Applause." She sang better than Bacall (to less impact). She could've pulled off the numbers once in studio; that was never the issue, as many note.
"I'm a comedian, but in my spare time, things bother me." Garry Shandling