See, my problem is in the stage version
All of which kinda negates the ending of the first play, AND makes Christine look like an indecisive ditz, and makes the Phantom look like a complete jerk again, totally wiping out what character development he had. (Never mind a classic 'you fail biology forever' moment as
for Gustave to exist Christine had to sneak out and cheat on Raoul with the Phantom THE NIGHT BEFORE THEIR WEDDING. And then the Phantom ditches her again for her own good.
unless the Phantom in his genius has invented paternity testing OR Christine and Raoul waited a month or two to consumate their marriage so she could be sure she was already pregnant there's no real guarantee Gustave is the Phantom's based on a one-night stand anyway. There's certainly no physical resemblance and love of/talent for music could have come from oh, I don't know, his OPERA-SINGER MOTHER AND VIOLINIST MATERNAL GRANDFATHER?
It's less that it's a stupid plot as it's an UNNECESSARILY stupid plot. The book was bad enough, the musical took the basic premise and went TOTALLY crazy (note, however, while IIRC the trigger 'man' is different the end result is the same.) It only functions if you accept every returning character underwent a radical personality shift, lost any sort development from the previous play, and learned absolutely nothing. Given the Leroux is in the public domain, there are a million sequels out there--they didn't have to go with such a weak idea to start with.