During Sarvangapushti Sthula Vyayama, changing wrist positions not merely cause change in the position of wrists, rather during change of the position of wrists, the entire alignment from respective side to other side from arms to lower limbs (legs) is changed and this change of alignment is necessary while changing from left to right side or vice verse, just to make the posture more convenient to perform. It is just like that we breathe out, for sake of making the forward bending postures more convenient (if we our lungs are inflated and abdomen is buldged out, we would not feel convenient to bend forward in padhastasana). No specific reason other than this, is there behind instructions for changing the wrist position during sarvangapusthi on changing side.
You can try without changing the positions of wrists, you will feel the difference between doing exercise as per the instructions and doing exercise without following wrist position changing instruction.
If you have still query related to this, feel free to write back here, I will be happy to answer or share my experience.
