Does wild and scenic river designation lead to increased river use and the need for a permit system?

There are no known studies comparing river use levels before and after wild and scenic river designation with changes in use levels of similar non-wild and scenic rivers. Factors other than wild and scenic river designation (i.e., river and water attributes, access to the river, and availability of facilities and commercial services) are considered to be the major influences on river use levels. For wild and scenic rivers, as for other rivers managed by federal agencies, the implementation of permit systems or other limits of use are typically undertaken when use exceeds an acceptable level or carrying capacity as determined through an agency’s planning process.

Source
Interagency Wild & Scenic Rivers Council