I drove it probably 20 times last year, and had two concerns. One night, a sudden snow covered the road and I nearly had to pull over and wait for rescue - I was driving 10 MPH and depending on the rumble strips to stay on the pavement. There was no one out there with me, literally no tracks to follow and everybody gone. It got scary until the rain resumed.
I-10 can be a lonely road. One "morning" about 4AM, I left Fort Stockton traveling west, and drove 45 minutes before I saw another vehicle on the interstate.
Naps at rest stops, "emergency" pull overs for sudden sanitary requirements, load checks, etc. I never had any reasonable fear of traveling I-10.
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.