What does it mean to control a border? To me, "border control" means to control who and what can cross that border in either direction. For example, I control the border of my apartment. It's largely up to me to screen who I can bring into my apartment. If I want to bring a black woman home on a date, there's not much my neighbor can do about it. Or a gay man. Or a mariachi band.
Now, my control of my border is not absolute. I can't bring home a prostitute. I can't invite customers without a business license. The number of people allowed is limited by zoning restrictions. I'm not allowed to bring dangerous chemicals. Once there, the people I invite can't be too loud, or shoot off guns, or damage the property. Most of these restrictions are intended to address the negative externalities that I may impose on my neighbors--noise, pollution, physical danger. And they may or may not be the best way to address those negative externalities. But note that to the extent that I'm restricted, I no longer control the borders of my property--the zoning board of my local municipality does.
But there's wide variation in the laws. If I don't like the zoning restrictions where I live now, I can move to a town with zoning restrictions more to my liking.
Move out to the country, and I can shoot guns, host raves, or blow things up real good. Move to Palo Alto, and I can be assured of carefully manicured streets, "smart growth", and good schools--albeit at a hefty price tag.
As a result of this variation, people with different risk profiles and aesthetic preferences can find communities that satisfy their desires.
However, suppose that we had national zoning regulations. Suppose that no matter where you lived--whether it be the Bronx or Butte--you would be governed by the same zoning restrictions. There would be constant battles in Congress over who got to define the zoning regulations. If the city people prevailed, those in the Bronx would be happy, but those in Butte would be angry as hell. And likewise for the reverse scenario.
And what of the special interest groups? Who would be surprised to find that many a senatorial campaign was financed by the National Association of Realtors? Or that Christian fundamentalists got laws passed banning adult bookstores?
Would you want Congress to decide who was allowed in your house, or how many people you could host? After all, the more decisions that are made by the national legislature, the fewer decisions that are up to you. And to try to change laws you disliked would be a massive undertaking, requiring millions of dollars and a national political campaign.
With respect to the immigration debate, the assumption by "border control" advocates is that the national borders should be the point at which immigrants are screened. However, what evidence is there that this is the optimal point for screening? How do we know that the state or city level wouldn't be the best level? Or, as free movement advocates suggest, at the individual level?