Yes, there's no absolute cutoff at, say, 3-5khz. But a device that's down 20-30db by 6-8khz, as most AM radios are, is NARROWBAND. You can't hear highs. Sibilant sounds are muted. Things like brushed cymbals, and tinkling bells all but disappear. This is real, and obvious. OBVIOUSLY we need better AM radios! Adherence to the NRSC pre-emphasis/de-emphasis should have been MANDATORY (rare is the FM radio that doesn't follow the de-emphasis curve closely).
But the combination of muffled highs (which manufacturers claim is to reduce interference...ok, it does actually do that) and rolled-off lows (w.t.f.? This is UNNECESSARY by any standard!) results in audio more akin to a telephone than anything "high fidelity" in too damn many AM radios. If your response curve looks like an upside down smiley curve, peaking in the midrange, and drooping at either end, then it DOES make discerning differences in fidelity at the station difficult.
In my own tests with an rf generator, I have found many AM radios in my house that can reach 8khz. But at this frequency the level is VERY attenuated in all but items like the GE SuperRadio (and the Radio Shack clone), and the Sony SRF-A100. As Orban pointed out in the 80s, it IS POSSIBLE to get 8khz audio out of typical AM radios, but it requires such extreme equalization that loudness is compromised, which of course compromises coverage, and "dial presence".