The relay keeps the speakers disconnected until the amplifier stabilizes. This delay is R010, C024, Q005, and Q006.
If you move the relay to the power supply, then the speakers won't be protected while the amplifier's bias levels are settling. Since the output stage is DC coupled, this could be anything, including one of the supply rails, far too much for the speakers.
If you do move the relay in the power supply, in a fault condition the speaker protection will be delayed by several seconds while the filter capacitors dump their charges into the poor speaker.