The reasons for free entry to the national park date back at least to the 1930s. The land that is today Great Smoky Mountains National Park was once privately owned. The states of Tennessee and North Carolina, as well as local communities, paid to construct Newfound Gap Road (US-441). When the state of Tennessee transferred ownership of Newfound Gap Road to the federal government, it stipulated that "no toll or license fee shall ever be imposed…" to travel the road.
At that time, Newfound Gap Road was one of the major routes crossing the southern Appalachian Mountains. It's likely the state was concerned with maintaining free, easy interstate transportation for its citizens. North Carolina transferred its roads through abandonment, so no restrictions were imposed.
Action by the Tennessee legislature would be required to lift this deed restriction if Great Smoky Mountains National Park ever wished to charge an entrance fee.