The undercarriage/suspension/frame damage is usually, as has been stated, from -extremely- rough dirt roads. The desert mountains are extremely rough on the roads, which cannot be paved. What land along the border that isn't private property, along with the property rights that follow, is either "owned" by the Bureau of Land Management or the Forest Service (national parks and the like, see south-eastern Arizona), who usually won't permit so much as a road grader or front-loader to fill in the washouts, much less install improved dirt roads or (gasp!) pavement. I've seen some really weird things happen to trucks, to include a drive shaft falling out of an F250, as the bolts and mounts securing it rattled out (was "manufacturer error," as they weren't torqued -quite- enough; had it been a pavement-only or a dirt-seldom vehicle, it never would have happened, but the rough roads that are a daily condition of the Border Patrol sort of point out "little things" like this).
The "entire lower half" of the bumpers being missing on Tahoes, Suburbans, and Chevy pickups is because it's cut off. Chevy puts plastic bumper covers on their vehicles, which often get cut/slashed/cracked/torn on the rough terrain. Removing the lower half of these prevents most of the damage, and allows a greater "angle of attack" for the front tires when going through the bad roads.
The rest of the bumper damage, as well as the body panel dents and dings, is often from brush: mesquite, creosote, and the like. As the roads cannot be graded or improved, the desert scrub is free to grow into them. The only way to "cut it back" is often to run it over or sideswipe it, just to get past. Driving around is often not an option. The ranchers, landowners, BLM, and USFS throw an incredible fit if they find that "vehicles have deviated from established roads" and fine the Border Patrol tens to hundreds of thousands of dollars. So rocks, brush, and other obstacles either have to be driven over, or moved by hand, not an option when dealing with large rocks.
The interiors get trashed from normal use, and yes, sometimes from abuse. The seats get torn from duty belts and other gear, rubbing along the seat covers. Plastic trim gets sunbaked, cracks from vibration, and falls off/out. Dash displays get busted from bouncing around. Sometimes items which cannot be secured, as there is no "mount" for it, goes flying, and hits stuff (agents included). Often, things that break, but are still attached in some way, and are not essential to the operation of the vehicle, get ripped out and thrown away, to stop them rattling/getting in the way/landing in the agent's lap. With all of this, sometimes you do find intentional damage, as there's a "why not, it's trashed already" attitude. Most of the time, though, the intentional damage happens -after- the interior is already "damaged beyond retail value."
All of this doesn't include damage that can happen from "unusual" incidents; deer/vehicle collisions are not uncommon. Neither are cow/vehicle collisions; here in New Mexico, there are some highways that are open-range, and the cows are free to stand in the road whenever they want. It might seem a simple thing to dodge them; it's not, when it's 12:30 AM, out in the middle of nowhere, and the cows are jet black, with so much dirt and grime in their coats they're literally invisible until they look at you and the reflections from their eyes become visible. Often they only look at your car when it's already too late to dodge or slow down.
None of this is reason for APCs or other similar vehicle types being purchased by law enforcement agencies, who frankly don't need "battle wagons" except in extreme, rare, circumstances. Rather, it's an attempt to explain the damage and destruction dealt to some vehicles seen at auction, and is therefore a diversion from the real topic.
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Frankly, I wouldn't -want- those armored tin cans out in rough terrain; getting one of -those- unstuck from mud, or a high-center on a boulder, would require some serious equipment, and not just a tow-strap or a chain!