Banning illegal aliens from wiring money would likely just change how they send money back home.
I'm also curious how they would expect the wire companies to verify that their customers are in the country legally.
This might be possible once States start requiring that people prove they are in the country legally before getting a drivers license, but until that happens, it's going to be very difficult for a wire transfer company to enforce this.
I would support legislation that would require a drivers license that conforms with the Real Id Act to send wire transfers or open a bank account, but until the Real Id Act really goes into effect, I'm not sure this is really practical to enforce.
I like the idea in general, I'm just not sure it can be implemented yet.
You are right, they can in some cases do that. But it's like the point made by the person who said they would use PayPal, yes in some exceptions they would. But why do you think they go to the wire transfer places in the first place? Because it allows them to anonymously/quietly wire money back in a convenient way without detection by the authorities.