Actually, nobody I have read so far has brought up one very good reason for this program: identification.
My daughter is a cop in a Western city with a big illegal immigrant population. When she arrests any of them, she finds 20 different driver's licenses and forms of ID in their pockets - with 20 different names.
Many of the illegals are quite law abiding (except for occasional public drunkennes or domestic violence), but some are gang members and thugs. However, it's very hard to find out who's who, since nobody has any reliable identification. In addition, the Mexican government has not been cooperative, because, quite frankly, our not being able to reliably identify the criminals among our immigrants and kick them out has enabled Mexico to get rid of some of its criminal problem by sending it over the border.
I think that registering illegals and giving the honest working people among them some sort of working papers would enable us to finally collect reliable identification information on them. It would also enable us to sort them out a little better, and perhaps even to put pressure on Mexico to be more responsible.