This is a very bad idea which will only drive the illegals to look for ways to send money which are not taxed. The obvious beneficiaries would be the drug cartels who already have methods of illegally transferring large sums from their customers in the US back to Mexico. Just open the pipeline a little wider and, behold, they are now in the banking business. Exactly the outcome we don't want.
Instead, something much more reasonable, like a 5% tax, might produce grumbling in the illegal community, but is a small amount for the assurance that the other 95% of the money will get there. The tax must be small enough that the cartels will not find it profitable to provide an alternative service. Otherwise we just strengthen the criminal element.
“Instead, something much more reasonable, like a 5% tax”
You need to read the IRS regulations regarding lump sums of untaxed funds. If you hit the jackpot in Las Vegas, the casino is REQUIRED to remit 50% of your winnings to the IRS. It is then up to you to file your tax return and let it be the determinant in exactly what you owe. The Drug Cartels are a separate issue, and denying Mexico half of the amount of all remittances would put a serious hurt on their economy, which is what we need to do. Frankly, I don’t see the cartels getting into the wire transfer business. There are already a bunch of them around beyond Western Union. All you have to do is drive by a Mexican market, they have signs up offering to send “envios a Mexico!”