Disclaimer: there's a lot of generalization here.You've only got half of the domino effect. Sure, it might become easy from a paperwork standpoint, but supply/demand will kick in and wages will drop.
In most countries recruiting immigrants is a royal pain in the ass. The main redeeming factor is that in the case where the immigrant's primary motivation is entry into the country (aka a work visa), the recruiter has an excellent negotiating position, especially when the visa in question keeps the immigrant bound to the sponsoring company.
Emigrating Americans are a little different, however. We're pretty highly paid in comparison to the rest of the world, and we're usually quite happy to stay in, or return to, our home country if we can't find something that suits us. Couple this with a good education and success in American industry, and this gives us a pretty powerful negotiating position in comparison with other immigrants. We still might not get anything comparable to an American salary, but at least we're able to negotiate rather than just having to accept whatever is handed to us.
This changes as soon as you remove the safety net. If there isn't a huge outflow of Americans, those who are emigrating because they truly want to leave America can just bluff their way through it. If there's a huge outflow however, this negotiating position will quickly be lost, at least in the countries to which most Americans would wish to be immigrants.