Hello Missi,
There are several reasons to come out of the asana practice in the way you illustrate. First, it should be clarified that there is no “always”. For example in this case it would not be appropriate for a pregnant woman to roll to the right. Instead she should roll to the left. So as Willem has kindly pointed out, it “depends”.
Seeing as how you’ve asked about rolling to a particular side, but contrasted that not with rolling left but with rolling up, I should explain the purpose of rolling to a side at all.
An appropriate Savasana provides the room for the student’s nervous system to shift to a parasympathetic state. That is a sate of ease - lower heart rate and blood pressure, stimulation of the digestive processes, lower body temperature, release of endorphins. For this reason it is imperative that students come out of Savasana gradually, slowly, with no hurry or jarring action. Additionally, rolling to the side and pressing the floor inhibits tension in the neck and lower back.
As to the right side over the left…
This brings the heart on top, regulates the pulse, prevents compression in the heart, frees up the nadi (channel) associated with the left nostril, and it is the auspicious side to boot.