I think Weber had received better reviews for his shows in LA (Phantom in particular) and wanted to open a production there to help ride the wave of good press pre-Broadway where people were sometimes hard on him.
Looking over Close's credits she wasn't quite the movie star people make her out to be now. Yes she had the huge hits on her resume but they were like 4 or 5 years prior. She was in a bit of a career slump when she took Sunset. She did win an Emmy but I'd think TV was still a step down for movie stars back then.
As people have said I bet ALW never thought that Close would upstage Patti. (Close probably didn't either.)