John Willett said it: Digifish said it.
Phantom powering was a major chaos reducer in studios. When it started to be used in the mid-sixties, the transition in condenser microphones from tube to solid-state was just underway. Tube microphones used multi-core cables with audio on one pair of lines, the plate and filament voltages on (generally) two others, plus shield and ground. Obviously their connectors had more than three pins, but there wasn't any one standard for the cables or power supply voltages.
Meanwhile, dynamic microphones already used XLR-3 cables like those we would use today for almost any professional microphone (or in West Germany, miniature 3-pin Tuchels). And some of the earliest solid-state condenser microphones used a system called "parallel" or "T" powering, which was developed mostly for the Nagra portable recorders used by film sound recordists. John's company played a big part in that. Parallel-powered condenser microphones used the same type of cables as dynamic microphones, but the powering system itself was totally incompatible with dynamic microphones--if you left it on by mistake, it could instantly destroy a ribbon mike or even a conventional moving-coil dynamic.
So the two very welcome advantages that "phantom" powering offered were that (1) it worked with the same, ordinary cables that were already being used for dynamic microphones, and (2) you could leave it on all the time--if a microphone needed phantom powering it would take it, while to a balanced dynamic microphone, the voltage seemed not to be there at all. That latter feature is the "phantomness" of the system--it's both there and not there, as required.
--best regards