The driver sleeps in the truck in neither of those scenarios. The driver drives back and forth from the port until his shift is over, then another driver takes over. If the truck breaks down ... you're in the middle of Los Angeles. Someone from the company picks you up, and you drive another truck, or go home.
GP's (very reasonable) thesis is that these are for truck driving as a day-job, in fair-weather locales, which obviates most of the complaints.
Not even, though. GP mentions the NYC metro area. I wouldn't call that a "fair-weather locale" in the winter. All the snow-related complaints seem to apply here.
I mentioned 3 trips a day because you could wake up in Los Angeles, drive deep into the inland empire, drive back to Los Angeles, and then back into the inland empire again. This was the context mentioned by an earlier top-level comment: https://news.ycombinator.com/item?id=33926883
You are quite right that running into problems in the Los Angeles is only a minor inconvenience. Having worked at both ends of this route, I regret to tell you that the other end is not the most welcoming environment. You probably wouldn't be out there too long if you did break down, but the desert gets pretty chilly at night.
GP's (very reasonable) thesis is that these are for truck driving as a day-job, in fair-weather locales, which obviates most of the complaints.