This is a very simple design for a phantom supply. This design will work with microphones that have no problem with the phantom supply being only 15V. It also has to be noted that, at high SPL, distortion can become intolerable (totally depending on microphone design). In that case, the phantom supply voltage has to be increased.
Now since the question was for a simple phantom supply, fed by batteries, the choice was made to use 2 9V batteries (since a lot of microphones can be run from phantom voltages as low as 10V). Another option would have been to use an array of batteries un