Without a doubt a hot political issue in this country. To some extend true as I recall the amount of paperwork my company lawyer had to file for my Green Card. However, I'm not sure that the original poster is getting screwed - he has just got a visa that has some annoying rules to it and many visas have such rules. No doubt the immigration system here could do with some reform.
However, about illegal immigrants not sure how much of this is true although I've heard some say these things. As for free healthcare and welfare - highly doubt it - how can they get free welfare without an SSN. And as I recall you do need to go to the SS office with the correct documentation to get the SSN - at least this is what I recall.