1) No one in American is required to carry proof of citizenship or legal residency.
2) SSNs can be made up on the spot, and money transmitters have no way to validate them.
3) Taxing money transfers would create black market opporunities for ethnic criminal organizations.
So it sounds good on the surface, but like all things immigration won't work without a national ID, which most oppose and is impractical in its own right.