Roughly a decade ago, I spent a year in a developing country working on a project to promote human rights. We had a rotating team of about a dozen (mostly) brilliant local employees, all college-educated, working alongside us. We invested a lot of time and money into training these employees, with the expectation that they (as members of the college-educated elite) would help lead human rights reform in the country long after our project disbanded. I got nostalgic and looked up my old colleagues recently. Every single one is living in the West now. A few are still somewhat involved in human rights, but most are notably under-employed (a lawyer washing dishes in a restaurant in Virginia, for example).
I'm torn on this. I'm sure my former colleagues are happier on an individual level. Their human rights are certainly better respected in the West, and the salaries are better. But the potential good that they could have done in their home country is (probably) substantially higher. On my way out, I signed letters of recommendation for each employee, which I later found out were used to pad visa applications. (I am perhaps feeling a bit of guilt over contributing to a developing country's "brain drain" as a result.) After I left, there was a blowup between two of the Western employees over whether to continue supporting emigration. The TL;DR of the disagreement was "It's the nice thing to do, and refusing to support emigration could reduce morale and our ability to hire go-getters" versus "We can't have lasting impact if our ringers keep leaving."
I'm curious about what other EAs have seen in their orgs. Is there any kind of organizational policy that exists on matters like this?
Yes and no -- the only concrete thing I see @WillieG having done was "sign[ing] letters of recommendation for each employee, which I later found out were used to pad visa applications."
I would find refusing to write a letter of recommendation on "brain drain" concerns to go beyond not funding emigration efforts. I'd view this as akin to a professor refusing to write a recommendation letter for a student because they thought the graduate program to which the student wanted to apply was a poor use of resources (e.g., underwater basketweaving). Providing references for employees and students is an implied part of the role, while vetoing the employee or student's preferences based on the employer's/professor's own views is not.
In contrast, I would agree with your frame of reference if the question were whether the EA employer should help fund emigration and legal fees, or so on.