Most of the reasons that the Open Borders enthusiasts trot out are selfish: cheap labor for large corporations, cheap labor for home renovations / housekeeping / maid service, and so on. If the children of these illegal immigrants will have more difficulty in school due to lack of knowledge of English or lower mean IQ, the enthusiasts don't care since their own children won't attend the same schools as those of immigrants -- and probably won't even live within 20 minutes driving distance of each other. So, someone else can shoulder the negative externalities.
One of the few reasons that appears prima facie not selfish -- the desire for all the world's cultures to "come together and get along" -- probably is selfish, even if to a far lesser extent. Women who say this tend to be interested in bragging about how multicultural they are, the better to make their female peers envious. The men who insist on this benefit, though, almost surely have something else in mind: the opportunity to date, marry, or just have sex with exotic babes. In most discussions of interracial relationships, the men in favor just seem a bit too eager to be guided by a dispassionate principle such as "It would be good if we could transcend race."
The trouble is that mass immigration makes interracial relationships less likely, as Steve has noted in his recent VDare column. The reason is pretty simple: people tend to prefer to date within their own group, but we all have standards -- if you're a Mexican girl who lives in a community where there are only 5 Mexican guys, it's unlikely that you'll find a guy who fits your preferences within your own ethnic group. Therefore, you'll be more likely to look elsewhere. But if you're looking for a 1-in-100 Mexican guy in a community made up of thousands of Mexicans, you're more likely to find him, or at least someone pretty close.
So, if you consider increasing the frequency of interracial relationships a good thing (for whatever reason -- although, be honest, it's probably out of a hope to date exotic hotties), then you should favor immigration restrictions. On a personal note, my first girlfriend was Central American (probably Salvadorean), and she sought me out -- girls asking out guys is rare in itself, let alone across racial boundaries! That was in 6th grade, or 1992, about six years after the 1986 amnesty; if I had been born five to ten years later, I probably would have experienced no such thing, since the ranks of Central Americans in the US had swelled by then. In high school, a south Indian girl and I had a light mutual crush on each other, which didn't go anywhere, though she ended up dating a White guy still. That seems much less likely these days, since there are cities where South Asians congregate to raise their kids; and upon graduation, many South Asians end up in the same big cities, where they have plenty of opportunities to date within their race.
My second girlfriend, in 1997, was half-Anglo and half-Persian; I would guess her parents met in the mid-to-late 1970s. Although there are a lot of Persians in Los Angeles, it's hard to think of many towns that are predominantly Persian, to the same extent that some towns are highly South Asian. At the same time, I do notice that the Persian high schoolers I've tutored, as well as the Persian friends they tell me about, are more ethnically conscious (they have more "Persian pride"). Ten years ago, you wouldn't have known who the Persians were at high school, even when there were quite a few (like where I went). Today, Persians are more "out" as a group, and so high school kids know who the Persians are, even ascribing stereotypes to them (which seem pretty true, as far as I can tell). Nevertheless, immigration from Iran is far less than from South Asia, and the pool of potential Iranian immigrants is swamped in size by the pool of potential South Asian immigrants. So, interracial dating between Persians and other groups seems pretty protected in most areas.
Now, dating prospects are just one force that might pull an immigrant out of their community; others are job prospects (where English may vs may not be required), and so on. All of these forces tend to cause a small body of immigrants to disperse into the larger community, in the same way that a tiny asteroid tossed into Jupiter's orbit would be torn apart and scattered by the tidal forces of Jupiter itself and its numerous large moons. Once the immigrant community attains a certain critcial mass, it can withstand these forces and maintain cohesion -- this simple logic is not lost on ethnic boosterists, whose primary goal is to increase the sheer numbers of their group. This is not out of a concern for the well-being of the individual particles composing the immigrant body, since they will continue to be constituted of the same elements even if the body is broken apart. Assimilation rarely means "fusion" or blending. This is most true at the level of genetics: inheritance is particulate, so immigrant genes will persist into future generations, rather than be blended into a homogenous mix with the native genes. I conclude that "maintaining group cohesion" arguments serve group interests, obviously enough. That's what we need less of, though: chauvinism.
I concede that aspects of the group's culture may be diminished, language being the most susceptible to loss, but we're not talking about the vanishing of such cultural elements -- they will persist as long as they will in the group's home country. Whether they vanish upon immigration to the US (or wherever) is of little concern to the preservation of such elements per se. Again we are led to conclude that if you consider preservation of a diversity of languages (or other cultural elements) a good thing, then you should favor immigration restrictions. After all, it's easier to preserve the Farsi language if most of its speakers form a country of their own, such as Iran, rather than immigrate en masse to a large non-Farsi-speaking country, where the language will be embattled at best. No matter how you look at it, all of the plausibly laudable goals that naive pro-immigration folks espouse would be better served by a far more limited immigration policy. The fortunate thing is that these don't-know-any-betters outnumber the cynical shills for corporate and elite interests, who would prefer to amass even greater wealth by exploiting imported peasants while socializing the costs onto the bottom 90% of the native population. That makes the solution to the problem rather feasible.