You are right, but so is the grandparent. A noise, click, or tone-based ABR is very basic in terms of measuring restoration of natural hearing. There are issues of rich spectrotempral aspects of speech, music, and natural sounds that (ideally) would be accounted for. Along with amplification and gain control, to which Outer Hair Cells are a major contributor in the cochlea.

There are various ways to measure these thing in animals and humans physiologically (ABRs, otoacoustic emissions, invasive and noninvasive electrophysiology), and with careful psychophysical experiments. None are perfect or comprehensive. Each method has its own strengths and weaknesses.

But it is indeed more complex than just testing a basic audibility threshold. The same issues come up with audigorams for hearing aid calibration and hearing in noise.