Europe has the "pie" in form of considerable (by standards of most of the rest of the world, including US) welfare benefits. I don't think it's particularly surprising that people who have access to it today don't want to share. The legal vs illegal distinction is really mostly about that - when it's legal, it can be significantly curtailed (and the same people who are against illegal immigration saying "just go through the process" tend to also be in favor of making that process much more difficult).
Unemployment insurance, free healthcare, and some form of guaranteed retirement income are nearly universal. To maintain these at the same levels, you need a certain proportion of people who work in relatively high-paid jobs and pay correspondingly high taxes. Which is precisely why immigration systems in most developed countries emphasize skilled immigration.
