John West's description of how and when/why the phone boots were used is accurate and correct.
John Craft's speculation is indeed correct about certain booths and/or hanging boxes being utilized not only for containing a dispatcher's telephone, but used as "test stations" for trouble shooting line trouble. At these selected locations, usually where the line departed from the immediate right of way for some distance, the individual wires were each "deadended" on "break-irons" on the pole crossarm, and insulated drop wire brought each direction of each wire down into the booth to knife switches so that each circuit could be opened to enable testing for trouble in either direction from that point. Also, if the pole line was downed by a snowslide or forest fire or some other disaster, all the circuits could be opened at the nearest test stations on either side of the fault so as to restore operation of those portions of the line not affected until the line could be repaired.
Having the test switches located in the booths saved the lineman time by not having to climb poles and physically cut the wires to make a test.
Some Test stations (like the one at Toltec) had the wires deadended on break-irons but the drop wires and knife switches were not used, The break-irons were "jumpered" by short pieces of line wire and connected with split-bolt connectors. The lineman still had to climb the pole (which was stepped for the purpose) to open the wires, but did not have to cut and re-splice them.