Two of the most dangerous roads in Texas are I 10 thru Houston and I 35 thru Austin. I will go 100 miles out of my way to avoid when towing. But they are not dangerious for the reason you think.
I would not hesitate to go thru south Texas or New Mexico during the day. Night might be a different story. I would not want to break down in those areas at night. I would carry some sort of protection, preferably a big pistolie or shotgun.