The "Phone Booth" has made it into most dictionaries, movie and TV plots and slang terms. (A "four-wheel phone booth" is CB radio slang for a person talking on a cell phone while driving.) An interesting legend is that Superman used a phone booth to change clothes. Actually he rarely used a phone booth for changing. For the full story check out Superman Home Page.
The cartoon "Captain Sprocket" made the idea popular. His only super power was a quick-change in a phone booth. That was a running gag in his comic stories from the early 1960's to 1984 in Archie Comics. Sprocket would often say, "Every hero uses a phone booth to change."
When public phones became practical, they needed to be protected from extra sound during use. The simple solution was to put them in a booth with a door. As phone technology improved, a booth wasn't needed to protect the phone, nor was sound too much of a problem. The phone booth, gave way to a phone with just enough shelter to protect the phone. As far as the public utilities were concerned it was just a public telephone. When the industry went into de-regulation, any company could get permission to operate a public telephone. Some even had a logo that looked very much like the local utility company (in Santa Cruz County, Pacific Bell). During the end of the 20th century, the cellular phone became popular enough, that public phone could be eliminated in many places.
According to PUBLIC UTILITIES CODE 728.3 (a) No telephone corporation operating within a service area shall remove any public telephone unless it has posted on the public telephone for not less than 30 days a notice, in a manner and form approved by the commission, indicating that the public telephone is to be removed and containing the appropriate telephone number of the commission which a customer may call for further information. (b) This section shall not apply when a public telephone is removed for public safety or public nuisance purposes or at the request of the owner or lessee of the property on which the public telephone is located.