The first-century C.E. Roman orator Quintilian nicely described the social function of this Roman mode of execution: “Whenever we crucify criminals . . . [we place them] where the greatest number of people can watch and be influenced by this threat; for every penalty is aimed not so much at the offense, as at its exemplary value.” - Paula Fredricksen, When Christians Were Jews. 

My commentary: Agreed, the cross of the Christ has exemplary value for all of his followers.