I believe it has to do with being seen as more "mainstream" and a certain respectablity that would come with being a NGO... not only that but also associated with the DPI (Dept of Public Info), actually building a "grassroots support for the UN".
This could be perceived by governments (that the WTBTS wants recognition in), that the Society has connections (within nations that recognize the WTBTS as a religion) and some "weight" behind it in influencing its membership. It is a political alliance and is recognized as such.
My thoughts. I work for a large corporation, and the more I study the moves of the WTBTS - 'cause God knows I didn't when I was an active JW - the more I see it for what it is... big business, making big business decisions, with all the office politics and media, legal, etc. that supports CYA.