I don’t know what “tonal density” means, and all this seems quite theoretical (not that it’s always a bad thing - but I think here she is blowing hot air).
She is not blowing hot air, to the contrary. Tonal density is fundamentally important and something that I always check for with every change to my system (including acoustics and speaker positioning).
Greater tonal density usually means more weight and harmonic completeness, richness of tone.
A particularly important marker for it is found in the lower midrange, something that has also been called the "power range" of an orchestra (think low brass, for example). Weight and richness in the low midrange are also important for the weight of the left hand of piano and for cello, to name two more examples (out of many that could be given).
Yet tonal density is also important for the "thickness" of sound throughout the midrange, including upper midrange, and in the treble. You could argue that it plays a role for the bass as well *) (even though excessive "thickness" there is counterproductive).
When comparing unamplified live music (in an average, not bright sounding hall, that is) with home stereo it is often the case that the home system sounds "thinner", i.e., with lower tonal density.
Preserving tonal density to a maximum extent possible should be, in my view and that of many others, a prime objective for a relatively realistic sound at home.
What Karen Sumner correctly points out is that in the search for "detail" often a thinner sounding midrange is preferred by system owners, but that this cuts against realism.
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*) Especially rock music needs a solid and weighty (even though at the same time rhythmically agile) foundation in the upper bass and mid-bass.