I just listened to that song and I can think of two reasons why they would only play it once:
1) It's eight minutes long.
2) It has the sound of a real siren at 3:07. The FCC has received complaints about the use of siren sounds over the radio as it coudd cause a driver to slam on the brakes and cause an accident. While they didn't outright ban the practice, they essentially told the radio industry "Ok, you can still do this, but you must use common sense."
There was a 1970s song (and an earworm) called "Indiana Wants Me." The repeated use of sirens in that song caused complaints to the FCC. As a result, the record producer released another version without the sirens for radio use.