Searched images of the GDMBR and there is plenty of rough terrain. 950 miles of paved road, with traffic.
I was a road racing cyclist before I went in the Army, I've ridden thousands of miles. I use to ride 100+ miles, from Springfield down to Branson and back in the morning with John Howard, Iron Man winner and Olympian rider (who is 4 years older than me and after riding neck in neck for 100 miles, he would out sprint me in the last 100 yards ). My road bike went everywhere, all kinds of roads, trails, fields and sandbars, even in the snow, we didn't have "mountain bikes". I probably have a thousand riding stories too.
Animals; Got clipped by a dear, almost hit a black bear, wiped out because of a cow and chased all kinds of dogs, even a fox.....yes, a fox!
Drivers; Seemed that out here in rural roads there was a sport called "run the cyclist off the road". Some kids even tried to run me off the road in town and a few got their doors kicked in. Some succeeded!
Road debris; I've run over all kinds of stuff on the road. In town I would draft behind trucks and doing that I couldn't see what was in the road until the truck ran over it. I had more damage to wheels and tires from road debris and potholes. Had a few wipe outs going around in a curve, usually downhill with some speed and bam, there it is, down ya go!
Weather; I'd ride rain or shine in the Summer and in the rain, sleet or snow as I got caught by the weather God. It can be freezing in April in Missouri.
That said, the reason I got bent out of shape about taking 4 small dogs on this grueling endurance ride is because I was a rider and I've had all kinds of dogs. It's bad enough having a dog in a vehicle on a road trip. Potty stops, get water, feed them, keep them warm or cool, keep them clean, keep them from being injured, away from other critters, and in some cases keeping them quiet.
This trip is not a weekend ride or camping trip in Mom's backyard. This route takes you through rough country, bear country, wolves, coyotes, snakes and other critters that 4 small dogs have no business being near.
And, if you're injured, can't ride, who takes the dogs? If one dog gets injured what do you do then?
What purpose does it serve to take those dogs, just to satisfy your ego, those are house dogs, they belong at home!
The pics I mentioned.