To your weight lifter analogy;
I would liken the weight lifter to the amplifier, the weight he's lifting to the speakers, and the power supply to how much muscle (power reserves) he has.
Theoretically, the more muscle he has (capacitance), the more weight (low impedance speaker) he can lift with minimal strain.
No, I would not, because they are really two units and both have to be up to par.
I'd say the muscles are the output stages (transistors, tubes, etc.) and heat sinks. The power supply is the stage he's standing on. Both have to be strong enough for the weight.
I'm adding heat sinks because they are a major enabler for Class A and A/B designs. You will melt your transistors without adequate heat sinks. Though truth be told the legal requirements to rate an amplifier n Watts may cause many amps to have exaggeratedly large heat sinks for music playing.