I'm not saying AOG that border control is an optional extra that should be dispensed with, but there is a frustrating tendency among many countries to view anyone wanting to travel there with some level of suspicion, particularly if such people want to stay. In addition I think you should be separating the problem of monitoring who comes into the country from the question of who and how many you should allow to do so. Illegal immigrants are an issue because they are hidden from the system, and then often end up in low-paid jobs are even criminal activities of one form or another. Immigrants in general can be very beneficial, bringing skills or trading knowledge and wealth between countries, and generally migration shouldn't be feared. The problem with various proposals for border control, though, is that they end up impacting on the people who are the sort you might want in the country while having little effect on illegal immigrants (who just sneak past the system anyway).
As I'm sure I've mentioned before, the spread of immigration in my department and around it is huge. French, German, Italian, Spanish, Swiss, Swedish, American, Mexican... but also Iranian and Israeli; a few from South Africa; someone from Brazil. A very international community, all friends, all working hard, all contributing positively to the nation (incidentally, the Brazilian is going to be kicked out in a year or so, because her visa expires and an unfortunate rule about having to spend a certain number of days per year in the UK overlooks the fact that her job requires her to travel to Switzerland to often to meet that target -- again, this serves to illustrate the point that immigration rules tend to hit the wrong people).
To be sure, a certain amount of border control is reasonable and while it can be a bit of a pain it's usually not to bad, at least for short-term travel. The main thing for me is not though to control borders in the sense of limiting numbers, but to control them in the sense of better monitoring of who is coming to the country. Many people have the first in mind -- I prefer the second, and hope that's reasonable enough.
That's not at all a brief reply, and I was intending to be brief this time. Must stop rambling on. Oh well.