"Were Paige or Streisand unable/unwilling to open the show?"
Paige was unknown in NYC. Streisand wouldn't have done the show for any price. She wants control of everything she works on.
Patti was the logical choice because she was known both in London and Broadway. Of the other choices, Betty Buckley was a bit too "cray-cray" to create the role. Once the role was defined, then she could come in as a replacement.
Andrew Lloyd Weber had to tread carefully because he had already created a firestorm by bringing his wife in Phantom of the Opera and then using her as a replacement in Aspects of Love. The leading lady had to be someone Broadway approved of.
But he once again created a firestorm by opening the show in LA rather than Broadway. And surprised people by casting Glenn Close whose singing ability was always questionable.
If anyone ever tells you that you put too much Parmesan cheese on your pasta, stop talking to them. You don't need that kind of negativity in your life.