Note the lack of tempting opportunities on the other side of the bear pit.
Note also how bears tend to be large and rather obvious dangers (to most people, anyway), whereas mines tend to be buried under the ground, because their deterrent effect depends on uncertainty about their position.
specified the presence of a "warning, land mines" sign
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.
Unmarked minefields, or air-scattered mines of infinite duration, are the bad kind.
A well-marked, time-limited or centrally controlled minefield is generally much less dangerous, on par with a razor-wire fence. Functionally, it's a sentry system which can be turned off electronically (or by waiting past a certain date), or at worst, which is marked on maps well enough that individual mines can be removed safely by engineers.
Unexploded ordnance (i.e. bombs which you fire and which then fail to explode) are a bigger threat after a modern battle than US-style minefields.
A minefield is probably much less likely to be deployed for this than automated sentry towers, however.
We do this in limited areas already -- there's razor wire and other "obviously dangerous" stuff protecting power substations, subways, power plants, etc. DoE-mandated security contractors will use lethal force at nuclear sites, probably with limited target identification.
I agree doing this over a 2000 mile border is a bad idea. For that, we should try to develop 0-50mi deep monitoring zone (depending on the area), with seismic sensors, UAV overflights, etc., and then whenever anyone is detected, send CBP/ICE agents to intercept. If they're innocent hikers, no harm done; if they're drug/people/etc. smugglers, detain and process them.
That's largely what we do now. The main issue is insufficient CBP agents, and no real consequences for illegally crossing the border ("catch and release"). I think punishment should be much harsher for anyone involved commercially in running the border, and somewhat harsher for people who do it repeatedly.
Ultimately the best solution is to make Mexico a less shitty place to be.
Well, that's all pretty reasonable, including the harsher penalties for people who run the border for a business, but still, seismic sensors and UAV overflights? That's just too close to home for me, I don't want a militarized border if it can at all be avoided. Aside from the monetary cost, I think it's detrimental to society -- is immigration such a bad problem that it requires that drastic a step?