I think it's a crappy answer too, but it's the one that'll work. Based on what evidence that it would work? This is not a scientific experiment here.
Based on what happens when we give aid to 3rd world governments, corrupt politicians steal it all and virtually none goes to the people. So if we did this, past experience would indicate that corrupt Mexican politicians would steal it, and we would still have massive illegal immigration.
Based on previous history of mass immigration into America. People will flee a country as long as they feel they can't feed they're family. Once the conditions in their home country get to the point that they feel there's the possibility of financial security the mass egress ends.
The problem with aid we give is we don't supervise it. We just shovel in the money. Always wrong. The money should be supervised.