Why emigrate?

So why would anyone leave their home and sneak into a neighboring country? They must be pretty desperate. No job prospects at home and an enticing hope in the neighboring country. Anybody with a good job and stable life wouldn't do this. Only the poorest (but ones with initiative!) would attempt an illegal border crossing to better their lives.

This means that these illegal immigrants are not only poor in comparison to their new country, they're poor in comparison to their old country. And if the average person in the old country is poor by the new country's standards, well, you get the idea.

Illegal immigrants are a strain on the governments (federal, state, local) for this very reason: they're poor. They're usually uneducated with no hope of advancement. Rich and middle-class people contribute more to the government coffers than they use, but all poor people (natives and immigrants alike) use more than the contribute. But that's okay. Taxes are just a form of wealth redistribution, after all. We expect this kind of thing.

But when the system is flooded with millions of new poor people, the system isn't going to like it. Taxes for the rich and middle-class have to go up to compensate.

How do we fix it? As far as I can tell, the best way is to get the immigrant's old country up on an equal level with the new country so he has no cause to leave in the first place. But if the government is so corrupt at every level that "rule of law" has no meaning, how can we possibly make a wealthy nation out of a poor one?

Perhaps the rich country can annex the poor nation, disband the poor nation's government, replace it with a better system, and start the poor nation on the road to prosperity. It would take a generation or so, just to get the mindset of corruption replaced, but it would work. True, the rich country would have to pay to support the entire poor country, but if millions are sneaking across the border to be supported by the rich country, what difference does it make? At least the poor sods will be able to stay in their home towns.