Thank you TeeCee
A perfect square wave at 100 Hz with p-p swing of 10 volts will have a RMS voltage of 5 volts (6.25 W into a 4 ohm load). A sine wave would only need a 14 volt p-p swing to produce the same RMS voltage. If you clip this sine wave off at 10 volts it will have less power, not more. In other words the unclipped signal from a more powerful amplifier will produce more power than the same signal clipped from a less powerfull amp (at the same gain setting of course).
Yes you will deliver more power when you drive the amp into clipping, you will more readily deliver even MORE power from a more powerful amp.
Everything else you said I agree with. However, I do not believe that high frequency components in the signal will cause your subwoofer to fail.