They're not unwilling
It's just that they don't always have the real-time morphing/fixing/sound better hardware available with the proper settings for every song in the trailer.
Because nearly none of them are actually "singers", i.e. people who can sing their own songs without instrumentation and not not only not be thoroughly ridiculous but also be heard by all the people in the room.
Today's "singers" are more along the line of "performers" - they "perform" the act of singing like a prostitute "performs" love. Some of them even mix the two to a certain extent.