They do - in their home countries. Fight for what you want in your home country. Don't go to other people's countries and expect that that country owes you something.
No, many times they don't. Reality is not so easy as what you seem to think.
Especially for people from "third world" countries tarnished by conflicts and poverty. Of course they will try to get a better life in other countries. What did you expect?
It's like, you're over 60 and born in the wrong country, tough shit?
Without delving too much into my job, I can tell you that the *majority* of immigrants coming in to the US through legal avenues are over the age of 60. It's considered the retirement plan - File a petition to immigrate to the US, and when you get your visa, you can come to the US and suck up social security. Even though their sponsor is supposed to sign documentation promising that they'll take care of their relative, the majority of them don't, or will do so as long as they get access to those social security payments.
I searched for the sources for those arguments, but I'm not finding anything. Could you point me in the right direction? I don't get which departments handles immigration statistics in the US.