On-point, intelligible, and succinct. Thank you. Although the original conversation about this was with you, I was ambivalent about dragging you back in. Glad you jumped in.This was explained before, but I feel it need additional explanation again , with examples:
1. An active "satellite" speaker (here: Neumann KH 150) with ideally flat frequency response is capable of, for example, maximum SPL = 110 dB (with less than 3% THD) above 200 Hz, and SPLmax = 100 dB (with < 3% THD) below 100 Hz. Because active loudspeakers have internal amplifiers, maximum SPL is determined either by maximum available power from the amplifier before clipping or by maximum THD from the loudspeaker. Of course, asking (internal) amplifier to output more power lead to amp clipping and excessive THD.
If we use 100 Hz high-pass filter for that "satellite" and add sub below 100 Hz, available maximum satellite SPL above 200 Hz still is 110 dB (with less than 3%THD)!
Why then the "trouble" with adding the sub? Because sub can deliver more than 110 dB clean (<3% THD) SPL below 100 Hz, instead of 100 dB without it (sub). Now, we have clean SPL = 110 dB for all frequency spectrum (including 100 Hz), instead of only 100 dB at 100Hz without the sub.
2. Let say Neumann have made passive “satellite” model "KH 150 PASSIVE" with the same drivers and enclosure from KH 150, but with passive crossover. We can connect this passive speaker to 1 kW amplifier, but no avail - again, maximum SPL above 200 Hz still is 110 dB irrelevant of the input wattage (from the 1 kW amplifier), because of the 3% THD limit of the loudspeaker drivers! We do want clean and undistorted sound, don’t we?
Of course, 1 kW can deliver higher dynamic SPL peaks (than KH 150 internal amplifiers) above 200 Hz – but with higher than 3% THD (coming from the speaker, not the amp)!
What you explain here the second time is just as I had understood you in your original post. Hopefully this clarifies things for other users who keep repeating that crossing over lower frequencies would make the system louder. Now of course, adding a sub will make the total system louder, just like adding any other speaker would (but for lower frequencies). That was not the question.
If you don't mind, could you also address this premise that crossing over lower frequencies will somehow decrease the distortion of the speaker because it has to travel less? Because to me it sounds like loudness and distortion sort of go hand in hand. If crossing over lower frequencies could actually decrease the distortion of the speaker, then this would mean the speaker could now play louder to reach the same distortion level.