Except, of course, as bellboid has so elegantly elucidated, this simply isn't true.
Remember The Philippines, tbaldwin? You never responded to my posts elsewhere. Under the policies you espouse, the country would collapse and hundreds of thousands - probably millions - would starve to death.
There are some disruptions - nurses from The Philippines are attracted to overseas work and this can create temporary shortages. But what you may not know, is that some 50,000 peeps a year in The Philippines are starting nursing school
for the sole purpose of trying to get a job overseas. Many of these people could study other subjects, but (surprise, surprise,) nursing is one of the most popular choices of study in the country today.
Of these @ 50,000 peeps a year graduating from nursing school, many will leave the country, many will be unable to for a whole variety of reasons. The NET effect will be an
increase in the number of nursing staff available in The Philippines - especially once the overseas workers begin to return, as the vast majority always do.
Your "one trick pony" objection to immigration is spurious to the point of being ridiculous.
Woof