Sorry, that is just too much logic for a web based discussion. What are you thinking?
In seriousness, girl scouts is a hot mess. It will take a serious effort to recraft that into something approaching the BSA, despite how much the BSA has been watered down over the last decade or two. That means vision, drive and a lot of work. Who wants to do that? It is much easier to find a successful organization, claim discrimination, demand entrance and be granted access using the force of law and a governmental agency all the while lowering the bar because, well, those expectations for Eagle are mysoginistic and unreasonable.
The gay thing was over a year ago. Many troops in my area lost their charter organization because of it. LDS didn't jump then, but they were clearly getting uncomfortable. It was the more recent announcement to allow transgenders into BSA that seems to have pushed LDS over the edge and restructure their youth program. LDS is a big part of BSA funding. Big. If adding girls causes the LDS church to dump scouts completely, that will be a big financial hit for BSA National.