Police can't ask citizenship so why would Western Union be required to? They have bank accounts so just mail a check across the border. Besides, it's not like they don't already take wads of cash with them every other weekend when they hop back down to visit grandma.
Yah, they could just mail it. Make it illegal to transfer funds if not a legal resident. Then if check sent, cash transfer, gives a trail allowing the investigator to find them, charge them. Cash, could just scan letters for cash, same deal. If no return address, and cash mailed out of country, government seizes.
For the same reason your bank or credit union is required to report any transaction in your account totaling more than $10K to the feds---because it's (or would be) a law.