I don't think your analogy works. Illegals use wire transfers of cash because there is a giant underground cash-for-labor economy that they earn their income from.
Not a lot of illegal aliens with their Wi-Fi logging on to PayPal.
Kaloogian's proposal addresses the real problem, which is the millions who come in and work for cash and then send money home to relatives, family members, etc...
One doesn't need WiFi to use PayPal. All that's needed is a checking account (even that of a cooperating U.S. citizen) and a basic internet connection.
"Illegals use wire transfers of cash because there is a giant underground cash-for-labor economy that they earn their income from."
They also come into the post office and buy international money orders and mail them to Mexico. They go to convenience stores and buy money orders, specifically drawn on Mexican banks, too.
This is a stupid idea, and it won't work. It will merely make more paperwork for those who deal with this money. So Jesus is an illegal. His cousin, Jose, is a US citizen. So, Jesus goes with Jose to the Western Union and Jose hands the money over and sends the wire. Jose shows his driver's license or his passport, for Pete's sake. The money gets wired.
It's that simple. And for those illegals who don't have a cousin who is a citizen, some enterprising citizen will start a business taking the cash to the Western Union and wiring it off.
Dumb, dumb, dumb.
There will be, if you ban wire transfers.