Don't forget that the recipient countries of immigrants are brain-draining the countries they're leaving. Arguably those motivated individuals are precisely those that should stay in their country and make it less 'bad'.
The middle path is limiting (not ending) migration while actually trying to help these counties (in particular victims of one’s past colonial ambitions) through aid, investment, and free/subsidised education for their youth.
I say this as a someone who immigrated from a dangerous country to the first world.
The only way the current plan even approaches sustainability is if the brain drain on source nations is sufficient to keep them stuck and suffering. That should make it very clear that the humanitarian impact is a side effect and not the goal.
Selecting "the best people" is the often-overlooked step. A lot of countries just want to import cheap labor and get easy economic growth today, damned be the consequences.
But more importantly wealthy countries shouldn't depend on there being poor countries where women still have "too" many children but rather we should fix our own problems so we want and can have sufficient young people of our own (not said in a nazi way).
And we should also redistribute wealth so there aren't any poor countries to exploit for natural resources, crops and people.
Redistributing wealth will not make poor countries rich. Most poor countries are poor because of bad governance, corruption, political problems (including armed conflicts), culture, and geography. I support some limited forms of foreign aid but when we simply redistribute wealth it mostly gets stolen or wasted without achieving any sustainable improvements.