There is an information and availability API for the federal parks system. The more people build apps that people use, the more examples we have to demonstrate the utility of this API in providing better experience to the public, and reinforcing the "Govt as a platform, via APIs" narrative.
The Federal Parks system took the first step in creating an availability API (with an intention to open up bookings via API as well). California then forked the language (with minor revisions), so they are slated to have an Availability API "soon" (who knows when it will actually come). This sets precedent at the federal and state level for parks, and also establishes a data schema that all the other state, county, city, local govt parks can build into, which would allow us to have a fully integrated discovery system for the public when looking for places to get outside.
A big part of persuading governments to follow is showing examples of what's possible, and the Rec.gov information & availability API, however limited, enables 3rd parties to do just that.