These resources, particularly in machine-readable format, have been invaluable for the simulator community, and for simulated ATC in particular.

For an example, check out https://www.youtube.com/watch?v=vlauVZ_5Le0, a virtual controller operating a chunk of New York airspace. As he moves around the screen (for example, around 21:30), you can see he has various fixes displayed. Those will be important fixes from various approaches, and their coördinates will be coming from machine-readable data, ultimately (in the US, at least) coming from the FAA.

All of this is possible thanks to these materials, as products of the U.S. Government, not being subject to copyright in the United States.

I will say, one important thing that's missing is publicly-available mappings of three-dimensional airspace (latitude, longitude, and altitude) to ATC sectors, and mappings of ATC sectors to frequencies. If you had that, you could (for example) look at your flight's location (in FlightAware or the ADS-B Exchange), work out the likely frequency for the airspace, and (if it's available) listen to your flight on LiveATC).

Source: Was a VATSIM controller, controlling up to & including Indianapolis Center.