True, though I couldn't suppress a giggle at the the thought of some radio ranter getting upset if it included a Spanish translation, since the fence would be on US territory.
What you're ignoring is the fundamental difference between a natural danger which we mitigate to increase the scope of people's freedom (observe dangerous animals from behind a fence, skydive after checking the parachute, hike with the aid of a map and compass) and an artificial danger which we impose to obstruct or limit people's freedom.
Playing with a bear is only tempting to small children or someone who's functionally retarded. A small percentage of people are suicidal or stupid enough to kill or injure themselves by ignoring or circumventing protective measures but we don't consider their rights violated as a result; the ratio of zoo deaths:zoo visitors (or whatever) is so low that the social benefit far exceeds the cost. If people in Mexico felt no particular motivation to enter the US other than for tourism, then we would expect to see at most 21 deaths annually on the Mexican side (~7m border area population/~0.003% suicide rate). Interestingly, we could expect up to 75 on the US side (also ~7m border population/0.012% s.r.).
I'm not sure what we do with the bodies in this hypothetical minefield; perhaps leave them there as a warning, because we don't want expensive border patrol agents to die removing them for burial. sure, they could be issued with maps or the mines could be turned off remotely, but as hackers we can all see the potential security pitfalls in such safety procedures. Given past administrative lapses with things as important as nuclear weapons, it's clear that we can't trust anyone - especially not government employees - to maintain the security of our minefield, so it would be better to shred all our maps as soon as we've deployed the things. I gather this is often what happens in a military context. It's true that this might result in avoidable future inconvenience if we ever develop a more comfortable relationship with Mexico, since removing the landmines would be dangerous and expensive. It would probably be better to turn the fence into a tourist attraction - people could buy a ticket to climb into guard towers and machine-gun cardboard targets of border jumpers, say. This would eventually set off (most of) the landmines, and tap into the unexploited commercial potential of historical killing zones.
Returning to the possibility of people crossing minefields, economic opportunity is enormously tempting to people notwithstanding the possibility of danger: it is a fundamental driver of history. We have gone to the moon and the ocean depths, fought wars, and died in vast numbers in order to gain economic advantages. About 3% of the world population is estimated have migrated from one country to another for economic reasons, and of course people often migrate within countries - either freely, as in the US, or illegally, as in places like China where choice of residence is considered a privilege rather than a right.
The interior German border mentioned above was regarded as one of the most secure ever; it actually had minefields, as well as guard towers with machine guns and so forth, and only consumed about 0.4% of the DDR's annual GDP by the time the country collapsed. Despite this outstanding achievement, people still insisted on sneaking across it, to the tune of about 120 a year. The East German government had a plan to reduce this by adding more security, but postponed it for lack of ready cash. It's unknown how many people died; most estimates are in the low thousands. Not all went across the border on foot; some traveled in hot air balloons, some swam or used inflatables to travel by sea, and some were smuggled inside commercial vehicles.
Of course, a key difference is that the DDR was more concerned with keeping people inside while you are more concerned with keeping them out. Whether this will have much influence at the individual level is hard to say. Notions about all men having inalienable rights to life, liberty, and the pursuit of happiness have been responsible for large-scale subversive behavior in the past, and if anything, the popularity of such ideas seems to have spread since then. Clearly, these concepts of fundamental equality and inalienable rights need to be curtailed and decisions about their availability placed in the hands of qualified administrators, who can then issue them in projectile form.