It seems like collecting data on these remittances would provide great leads for ICE to track down illegals. How many actual Americans have ever used Western Union or other wire transfer services to send money overseas a few hundred dollars at a time ? For most actual Americans it is probably very rare or in large business-related amounts.
VERY true, an EXCELLENT idea.
I BET that ICE already knows exactly who is here and why. Our foreign workers already are "legion."