Headroom, mainly. Your peak voltage is 1.736 volt only when you have a sine wave signal of exactly +4 dBu (0VU on professional equipment). That never happens in the real world.. 0 on the meters is an averaged level, so with real-world audio signals you will have peaks far higher than 0VU.
A peak of +20 (+24 dBu) would result in 35Vpp output which would clip your +/- 15V rails...
600 ohm line driver IC's such as the SSM2142 have supply rails of +/- 18 vdc. The output voltage of this IC is +/- 10 volts into a 600 ohm load. These are often use for long signal runs, such as a 100 foot 'snake' from stage to mixer, or in some studios. This wide voltage helps over come EMI noise and 'ghost' sounds from adjacent channels. The extra high supply voltage is to account for the voltage drop you get on long cable runs to a 600 ohm load.
The receiver has balanced 600 ohm inputs that divide the signal by 2, bringing the signal peaks down to +/- 5 volts, well within the range of IC's that use +/- 15 volt supplies. This rather expensive setup is used mostly in studios that record in 24 bit SACD format(120dB dynamic range), the default format (after RSCC) for DVD and Blu-Ray audio tracks.
If the recording is a musical event such as a concert, another compressed version is made for 16 bit CD audio(90dB dynamic range). Third party studios will get the rights to make various grades of MP3 versions(14-15 bits dynamic range).
For each drop in dynamic range lower voltage IC's can be used. Todays best audio IC's run on 5 volts or even 3.3 volts, mostly for MP3 players, because newer technologies have pushed their noise floor way down, needing less voltage to produce about 60dB to 90dB of dynamic range.
The next generation of audio IC's may have 120dB of dynamic range with only 5 volts of power. Then the higher voltages will be found mostly in power amplifiers. The Cerwin-Vega Metron series has supply rails of +/- 130 volts for its 1500 watt mono-block amplifiers.