Wider shoulders would help, but in many places HWY 126 is bound by the river or deep ditches on one side and a steep hillside on the other side. It wouldn't be easy to say add 6 feet (total new shoulder, both sides) of shoulders to the whole road.
It may be easier and cheaper to do road improvement south of the river than fixing the shoulders. And, of course it would be much more pleasant to ride one's bike on secondary roads.
Wider shoulders, of course, would also be a benefit to vehicle traffic.