Can't explain what is right or wrong about the examples above, but just thinking about this logically... If you filter out part of the spectrum (any part), the acoustic power produced by the speaker will be lower. Since the efficiency of the speaker has not changed, the electrical power required from the amplifier must be lower - conservation of energy. However, as Ray points out, the peak voltage requirement will not necessarily change, and since voltage swing is is the primary determinant of the amplifier power rating (for a given impedance) the necessary power rating of the amplifier may not change. However, you may be able to get by with a less "robust" amplifier. Granted, some hand-waving in that last statement.
I can make things even more complicated for ya... but such complication is usually necessary
Ok, continuing from the previous post: Each individual component frequency of the square wave can have more higher peak amplitude than that of the square wave. Yet, when I sum the individual components together, I get a lower peak voltage, and consequently, a lower power too? And that confuses people.
The magic here is: The frequencies are antiphase with each other. Hence they cancel out.
Does that mean since they cancel out = their power or voltage or whatever requirement also cancel out? Not exactly.
Because we have to also consider the amp as something that can provide different amounts of power at different frequencies too.
An amp's max output power / an amp's output impedance is frequency dependent. Heck, a power supply's output power / output impedance is frequency dependent. More power supply capacitors = less LF impedance for example, more decoupling capacitors = less HF impedance etc.
And supplying power at frequency A may not affect the ability to supply power at frequency B. Although, of course, in this context, there is a high % of effect. At 100kHz vs 10Hz, then maybe not.
But point is, even the different frequency components may cancel out, it doesn't change the fact that the amp is trying to push power at different frequencies, each demanding performance from the amp in a different way. By HPF-ing, you are removing some of it.
Say we have to produce a wave. F1 (lower frequency) + F2 (higher frequency) gives a lower peak amplitude than F1 alone because F2 is antiphase with F1.
F1 is drawing power from the electrolytic caps, F2 is drawing power from the ceramic caps (or whatever decoupling blah). Even though the frequencies may be antiphase, the energy that would have flowed back to the electrolytic caps can't, because it is too high frequency, so it flows to the ceramic caps.
So even though the final voltage may be lower, I still need my amp to be able to produce each individual voltage component properly, and each individual voltage component can still be higher than the final voltage.
Or in other words,
The same amp that is able to reproduce one sine wave at amplitude X, may only be able to reproduce one square wave at amplitude Y, where Y is lower than X. So we're not breaking any physics rule nor layman thinking here. We don't need more power despite filtering, we just happen to need less in certain frequencies and the leftovers appear like that, but that doesn't mean we don't have to supply for these leftovers in the first place.