I know for an absolute fact that the off-bway production of SA was taped and is in the archives at Lincoln Center. I don't know if they taped the Broadway production subsequently.
I'd be surprised if PBS taped SA. Taping this production of Gypsy would be cool, but I'll survive without seeing it again.
"The reason that not ALL shows are filmed is simply due to costs. The production itself has to fund this filming -- Lincoln Center Archives doesn't do the filming out of the goodness of their hearts."
Actually, the Library IS the one that determines whether or not to record the show, and while they certainly will try to convince the producers to help cover the costs, if they want a show bad enogh they will find other funding sources.