Succah 56a - Shehechiyanu comes before Succah

Beis Shamai offers 2 arguments to explain kiddush before hagafen: 1. kedushas hayom is the cause to have a cup of wine. 2. Kedushas Hayom comes first with the onset of the day. the gemara is mechalek to make rabba bar bar chana who says Shehechiyanu and then Succah, fit with the first reason of Beis Shamai. The question is that rabba bar bar chana can work himself out with Beis Shamai very simply by saying that the second reason of Beis Shamai is the primary reason. Therefore, here too, shehechiyanu which is caused by the onset of the day comes before the chiyuv of succah which just comes when you come into the succah. Is the gemara struggling with rabba bar bar chana only bec. it wants to work it out with both reasons of Beis shamai (even though in beis hillel we only work out rav with one of the 2 reasons of beis hillel)?