That may be plausible. The reason I don't agree is because ALL conventional speakers have a falling frequency response (downwards treble tilt) the further you get from the loudspeaker.
A loudspeaker's directivity typically increases with frequency, bass is nearly omnidirectional, treble is beamed forward. That means the on-axis response and the power response (SPL averaged over the whole sphere, i.e. proportional to total radiated power) are not the same shape:
On-axis response: relatively flat, because the tweeter's high directivity concentrates HF energy forward, compensating for the tweeter's naturally lower output.
Power response: falls off toward high frequencies, because even though on-axis output is flat, the total energy radiated into the room at HF is smaller - it's just concentrated into a narrower beam rather than spread over the whole sphere.
In any real room (not an anechoic chamber), what a microphone picks up is the sum of two things:
Direct sound: travels straight from speaker to mic, follows the driver's on-axis directivity pattern, falls off as 1/r (6 dB per doubling of distance) - this component is flat/full-range because directivity concentrates the highs.
Reverberant sound: energy that has already bounced around the room many times before reaching the mic. Its level is nearly uniform throughout the room (roughly constant with distance) and, critically, its spectral content is shaped by the loudspeaker's power response, not its on-axis response - because it's the sum of energy radiated in all directions, most of which was never HF-boosted the way the forward axis was.
Close to the speaker, direct sound dominates, so you measure something close to the flat on-axis response. As you move farther away, direct sound keeps dropping at 6 dB/doubling while the reverberant field stays roughly constant, so beyond the room's "critical distance," the reverberant field which is treble-shy because it reflects the bass-heavy power response starts to dominate the total measured spectrum. The net result: high frequencies appear to droop as distance increases, even though the loudspeaker's directivity is, on-axis, doing exactly what it's supposed to do (keep treble output up).
So the apparent contradiction resolves once we separate two different "sound power" concepts:
Total radiated power at a given frequency (what directivity theory constrains) really is smaller at high frequencies relative to an idealized flat power response, precisely because of the high directivity - a directive tweeter has to work less hard to sound loud on-axis, so its actual power output is comparatively modest.
On-axis SPL stays flat close-up thanks to that directivity, but as the reverberant field (built from the low total power response) takes over the measurement at greater distances, the composite response sags toward the power response's shape.
Two secondary contributors compound this at longer distances specifically:
Air absorption, which scales roughly with frequency, becomes non-negligible over many meters and adds genuine HF loss with distance, independent of directivity or room effects.
Multi-way lobing/interference between drivers can also shift the crossover-region and HF balance depending on measurement distance and angle.
But in a typical room, the reverberant-field effect - driven by the fact that high directivity implies lower total radiated power even while boosting on-axis level - is the dominant reason a speaker's measured response tips toward bass as you move away.
