The rating of 1 Hz to 500 kHz is the rated power bandwidth. In all amplifiers there is phase distortion present within its rated bandwidth. That distortion is audible. When an amplifier is designed with a larger bandwidth the phase distortion is shifted to a higher frequency. The larger the power bandwidth, the further the phase distortion is shifted from the audioble range. Therefore, from the standpoint of phase distortion, the larger the bandwidth, the better. One of my former amplifiers (Adcom GFA-535II) had a bandwidth of up to 150 kHz.
