Lynn, recreational trails are funded through federal grants, grants from private entities, volunteer labor, and the work of trail user groups. Yes, state funds are involved as well. 
I don't know that I agree that this trail is the right move, but do believe the underlying rational is solid - outdoor recreation is a big business that positively affects communities involved both culturally and economically. A trans-Alaska hiking trail would be a draw to long distance hikers the world over, much like there are thousands of people each year who traverse the PCT and the Appalachian trails. Towns and communities along both of these trails have seen economic gains from the trails even in hard economic times. For people who hike these trails it is often a once in a lifetime experience that they save years to do. Flights, hotels, food, gear - all of the support industries would benefit. We need overall economic diversification in this state. Sometimes we have to spend to make.