I totally agree with you(and, I guess, with Prince)about Beth singing this incandescent song the moment she first appears. It has never worked for me. I'd be interested in seeing Frank sing it. When Mary sings it in the second act, it IS heartbreaking. SHE is a developed character we care about. Not Beth, at least not for me.
Maybe this is one of the(many)problems that the whole structure of the musical imposes. Too many nasty, unappealing and/or undeveloped characters in the first act.