This is not true, and let me educate you on the matter as a person who actually lives in LatAm and knows people who went to US illegally:
You need a lot of money to get to US illegally, the same amount you could use to start a small business in their country. If they manage to get it for travelling, they can get it to work. Thing is, they know that the job would make considerable less than in US or any other country, so they really rather risk their lives and take their chances. FYI, when I say it would make less money, I don't necessarily mean pennies. It can help you to live ok, but you can't afford luxuries and that's what many people want for themselves. So, when you say "better life", it's the same life they can have here, except it'd be faster in US, but not impossible to have in LatAm. The actual poor people who can benefit from going to another country have no money to get there in first place. They just have no way to get it. The ones crossing illegally are middle class people who have family support and aren't starving.
The best case scenario is people who manage to get their investment back and return to their countries and use it to start something with their families. The worst is that they never leave because the reason they go to US is not because they want to make more money, but rather, they want free stuff and think the state owes them that and don't care you are the one paying for it. They know they can exploit the system and have no qualms on doing it because they don't care. In fact, they will do their best to bring their families and say it's all fine because the government pays for it all. I know people who have said that personally to my face. The reason I don't tell them that they are exploiting Americans is because I didn't want to start a fight right there (reasons may vary).