The wealthy and connected elites are the ones with US visas from those dirt poor countries. No chance they will risk losing them.
I think it is the other way — those in power over those countries, they are all elites, not dirt poor — all have either Swiss or Caribbean bank accounts in millions, if not billions.
Those deported are criminals, so they do not want criminals back into their countries. These deported criminals are likely a threat to those elites.
Start with their UN delegation.
These are frequently the relatives of well connected politicians in their home country.
They are on the delegation so they can live in the US and receive a very nice living stipend from the coffers of the UN.
If they get sent home they lose that money and have to go back to their third world hell hole.
Even suggest that and these relatives will be on the phone home to their well-connected relatives screaming at them to take back these undesirables today.