If a "developed" country wanted to stop migration they would work to raise the living standards at the source. There is less chance of that happening than removing xenaphobic behaviour from the natives however.
Or the "developed" society becomes more brutal than the place the migrant are fleeing from, so they stay away out of fear.
Biden at least nominally adopted such as policy. See, for example, "U.S. Strategy for Addressing the Root Causes of Migration in Central America", https://www.whitehouse.gov/wp-content/uploads/2021/07/Root-C...
But, AFAICT, it's mostly been a quiet public-private approach that in dollar terms isn't very substantial. See, e.g., https://www.whitehouse.gov/briefing-room/statements-releases...
If you look at Haiti, Venezuela, etc, it seems the limiting factor here is an unwillingness of the U.S. to leverage any political muscle, either domestically or internationally. I presume that's partly a consequence of Iraq and Afghanistan, but also probably because for some large factions, especially on the left but increasingly on the right, in American politics any form of involvement is unacceptable. It's almost like a radical ecological argument: the rest of the world is in a state of nature, and any intervention by an external agency is per se morally evil; the moral imperative is non-intervention, outcomes are irrelevant. Even those who don't hold this belief (explicitly or implicitly) at least understand the consequences: any perceived failure in intervention will be blamed on them, and nobody wants to face the ire of the religionists.
The USA will get flack if it meddles and if it doesn't meddle, they really shouldn't worry about world opinion at that point. More to the point, it is impossible for America to fix the rest of the world, even if that were the moral thing to do. Welcoming some immigrants from countries having problems is probably the best we can do.
People being afraid of the warrior princess is probably a good thing.