Pressure measurement blood flow
You have a point there, but it probably does not play a big role. First one arm is not such a big branch, and then the carotids contain the main pressure "sensors", so the heart might just beat a bit weaker/slower. Resistance is higher, but demand is less. 

Compressions like that can happen all the time, through weight or muscle tension. If it is not both legs at once, this is only a problem for the blocked-off part, after a while.