I remember stopping for a nature break. IIRC, the land generally sloped down towards the river, steeply in some places. MDOT would likely have had to do a good amount of fill work to add a shoulder. Not only that, there are some stretches that already come very close to the bank of the river. If you look on Street View you can see several places (e.g., a bit east of Robbins Gulch Rd.) where if you added two or three feet to the river side of the road your supporting slope would be extremely close to, or even in, the river. Plus, you'd have to cut down trees and other growth that helps stabilize the bank. On the other side, you are hemmed in by the hillside. The further east you go, the more things widen out and the shoulder picks up again.
The next day I rode MT 43 to Wisdom after Gibbon's Pass. I don't think I got passed by one vehicle on that stretch and only saw a handful coming in the opposite direction. The only menace were the mosquitoes during the climb of that little lip maybe 5-6 miles outside of town. There is a ranch there. I think they breed and raise mosquitoes.