It's a failure of policy to be sure, but it's not as though planning is really at fault here, just as open borders isn't really a market solution (even though the implication that it is somehow worms its way into this argument). A market solution would be to use the government to perpetuate scarcity of visa slots and enforce property rights around a visa, and allow visa holders to sell or trade their visa rights. As a corollary, the problem with immigration is not inefficient allocation of slots caused by planning, its that we have immigration limits to begin with.

It's a neoliberal trope to try to work markets into every social problem, but this is really an issue concerning ethics and justice, not allocation.