I'm not sure I agree with your math, but for me, whether or not this makes sense to GE shareholders comes down to whether you think that the financial sector will or will not outperform large industrials in a rising interest rate environment. The fact that GE pays a great dividend and Synchrony pays none should also figure prominently in making an individuals' decision. The supposed "discount" means little or nothing to me personally. Just my two cents.
But even if the exchange is properly subscribed and goes through, doesn't GE still hold the lions share of SFY stock. Does GE just plan to gradually sell their shares as conditions, need and performance dictate? I'm not the brightest bulb, but at the end of the day it looks to me like GE will still be SYF's largest stakeholder by far. What am I missing?