The NPS doesn't want to deal with people breaking down out there or having to maintain the road anymore so they try and discourage motorists from using the "trail". Plus there's a lot of stupid people in this world, and they're being overly cautious as they always are.
I was just out there last month, and it's in pretty rough shape. That said, it's something I would have done in my stock WJ without really worrying too much about it. Properly prepared, absolutely, but it's something "Guzzler" could have handled just fine. What differentiates this road from the others in the park is the Black Gap itself, a semi-steep rock cut just about a lane wide and if I remember correctly about 40 yards long that has a wash-out at the bottom. It's this bottom part that's the problem. Obviously. It's usually stacked with rocks, but it still can have a nasty break over angle. I'd definitely would make sure you have skid plates if you're riding at stock height in the WJ, but it should be very doable.
(I like taking, and subsequently posting pictures so please indulge me. Besides, pictures make a post better.)
It doesn't look too bad in this photo really, but at least you get an idea of what to expect. It's nothing compared to anything you'll find in, say, Colorado, but it's the worst part of the Back Country road system in Big Bend.
The other concern with the road are the washes, they can sometimes be pretty deep. It's nothing that you should have too much trouble with... as long as it's dry.
My friend's 4Runner at stock height and street tires. No problems for him, so you should be alright.
It's really not that bad of a road, but you'll probably be the only one on it. So be prepared.
Flats can be common in the Park, so at least have a decent spare and probably even a tire patch kit and pump. It's at least a 12 miles walk back to the nearest pavement, so keep that in mind.
I stole this image from Big Bend Chat: (A good online resource)
I've been told that the easiest route is heading south to north and that's the direction I've taken it.
Don't let the term "Park Maintained" fool you, the back country roads are not your typical graded county affairs. They cant get a little rough. Nothing technical though, just some slow going and most are a single lane wide. So watch out for oncoming traffic at the corners.
About the other roads in the park I got to see last month:
is really loose, decent sized rock in stretches, but your 4WD should make easy work of it. It's especially narrow in places and as with most of the back country roads you can probably expect a couple pinstripes from the roadside brush after traversing it.
is rougher, but plenty solid. I could probably get a Honda up it. (Very carefully mind you - don't want to lose an oil pan)
is plenty wide at almost two lanes, but it's washboarded for most of it's length and populated with some stretches of rock. I've have
taken a Honda down this road with little issue.
River Road East
is nothing really to worry about, but River Road West
was going to be reworked after the beating it took in last summer's flood. Doing the entire length would probably eat up almost all of your day.
I have not yet driven Old Ore Road
(This was my third time to the park), but I hear that it too is an all day affair.
As advised on every pamphlet, map and website when it comes to these roads, check with the Rangers when you get to the park on their current conditions.
I'll add more to this response later, I need a coffee.