I've covered most of that route at different points, with one trip covering from Northern Canada to just shy of the Darien gap.. That trip I was driving an '85 S-10 extra cab 4x4 with a 5 speed and the 2.8. Other than an overheating incident due to a dust clogged radiator on a side trip to Baja, that was entirely my fault, the truck never let me down, and I rarely used the 4WD. I had a standard cap on the bed with a mattress and such back there. That was in the late 90's. Over the last 40+ years I've traveled extensively in Latin America, and spent some time living there as well.
I just did the last 2000 miles (roughly) of the southbound trip earlier this year, brought the wife and kids and met up with some friends in Buenos Aires and drove to Ushuaia in a pair of manual Diesel Discos the friends own. Saw lots of VW pickups, land rovers, and 4 runners when you got off the highways, tons of little Korean, Chinese and Japanese econoboxes on the highways along with all the commercial stuff.
At this point the roads in SA are much better than they used to be, we probably could have done all of the highway driving in a corolla, but the 4x4 let us get to some really beautiful and interesting places off of the highways in Patagonia. The dust, along with livestock and wild animals wandering onto the road were the only real hazards for most of the highway driving. Thankfully none of it ever turned into an issue for us. We did see the immediate aftermath of a little VW passat (I think) hitting a Guanaco at speed though, it wasn't pretty. I was immediately reminded of why the discos had large 'brush guards' out front.
We stayed in Hotels and homes along the way. Our friends made the arrangements. I wouldn't have minded camping, It was summer there, and camping wouldn't have been too bad, but the kids and wife were happier this way.
Honestly I suspect the most challenging part of the drive is still through Central America. The roads haven't gotten any better in the last 25 years, I think the corruption and bandits are worse, The mountain roads are some of the worst I've ever driven, made worse yet by the local traffic (chicken buses, I'm looking at you) and getting parts can take forever if you need them.
One day I'll run the entire route in a single go. Probably with a co-driver, and without the kids or wife. I think an old Disco or 4Runner would be good choices due to how common they seem to be for much of the trip. They don't stand out, and should be *relatively* easy to get parts for.