Why isn't phase modulation commonly used in radio stations?
There is actually little difference between FM and PM.  The reason is that when you change the frequency you necessarily change the phase to get there.  Likewise, when you change the phase you end up changing the frequency to get there.
Some FM schemes actually use PM and simply adjust the input signal to compensate for the slight difference so that the output ends up being exactly the same.
Why don't we use PM vs. FM?  Well for the commercial FM broadcast band, FM was chosen long ago.  If someone started broadcasting PM modulated music, it would sound funny on radios all over the place because they are expected FM, not PM.
Can PM be used for broadcast?  Yes it can and there is no reason why a band could not be created that used it.  But currently there is not such a band.  PM is often used by Radio Amateurs (HAMs) along with just about all other forms of modulation.  PM is used in your WiFi router, your mobile phone, and DBS satellite TV systems.