I have been driving the Big Bend area since I was born. My dad was a surveyor in West Texas in the 50' and drove a military surplus Jeep and then a Jeep Wagon. My first trip after I was married was in 1971. All of the park back roads were not maintained then and it was truly an off road adventure, since then I have noticed the park will maintain the roads every month or two so not much of a challenge unless there is some rain. But it ain't the challenge of off roading but what you can see on the back roads. It is chocked full of interesting sites and wonders if you take time to look and hunt. The River Road used to take 10-12 hours in the old days due to washouts etc. now it can be driven in 4 hours if you don't stop. Mom and I would spend three days on the River Road, camping and exploring. Take your time and don't hurry, just lay back and enjoy the Chihuahua Desert at a slow pace. Don't hurry through like the guys on Youtube. It is an experience like no other you will have.
I took my entire family out in March and it was a truly a relaxing adventure.