Emigration can alleviate unemployment in origin countries by reducing the labor pool and decreasing competition for scarce jobs. Between 2000 and 2007, unemployment rates in Central and Eastern Europe dropped by as much as 50 percent, in part because of increasing migrant outflows from these countries.
(Basic market principles, this - freedom of movement for labor is vital to achieving efficient labor distribution)
Successful emigration of skilled workers can sometimes encourage more investment in education, potentially raising a country’s overall skill level. Migration opportunities associated with nursing led to the development of a private education system in the Philippines that provides low-income women with career opportunities. Large numbers of nurses remain in country after completing their education, and as a result, the Philippines has more trained nurses per capita than some wealthier countries, such as Greece and Malaysia.
The idea that trapping people in their own country thinking that if they have nowhere to go, that will be better for the country than sustainable improvements in retention methods for skilled workers is just… not backed up by evidence.