I don't remember any white courtesy phone because I was not swank enough, not because I wasn't old enough.
I went to the Holiday Inn once a year with my parents and we went to Wisconsin Dells, or Niagara Falls or typical American family stuff in the 50's and 60's. No one had a courtesy phone. We had a phone in our room. It was the color of the room.
Yes indeed, they were in Airports, Hotel Lobbies etc. Have not seen one around since the 90's I believe.
If you name was called you were directed to the white courtesy phone in the airport, Grand Central etc
In a Hotel Waldorf, St. Regis or similar you needed to contact a guest you were directed to the white courtesy phone. In the Holiday Inn by the Pentagon there were a complete bank of them which were connected to the Pentagon Switchboard.