That's EXACTLY the problem. Arkansas has 16,400 miles of state maintained roadways, over 16,000 miles are 80,000 gross maximum weight roads.
The actual state statute says "The maximum size and weight of vehicles specified in this chapter (state statute 27-35-103) shall be lawful throughout this state, and local authorities shall have no power to alter these limitations, EXCEPT (my emphasis) as provided in this chapter".
It's their exception, not mine. They are legally required to convey the EXCEPTION message clearly, and either place the signs such that the road can be avoided, or provide additional signage to turn around or detour around prohibited roads.