Why do chords usually "sound better" to the human ear when using larger intervals between low notes and, smaller intervals between high notes?
Is it how the ear and brain register the harmonics?
This is a good question. The reason in short is that harmonics are not always in tune.
Note I am oversimplifying
Now imagine a chord C3 E3. The harmonics now come out as
Notice the huge difference between the E5 from C3 and E5 from E3.
a difference of 13 cents. In this case they are fairly quiet but the clash between them would still be audible.
The higher notes sound clearer to us because of several factors. The higher harmonics are harder to hear. They also decay much more quickly.
I have some software on my computer which I can use to visualize what I am saying.
Chords "point" at a common fundamental.
A power chord has frequencies (in terms of its fundamental) of (1, 3/2), making for a greatest common divisor (in terms of whole multiples, pardon the mathematical fuzziness) of 1/2, one octave below the fundamental.
A major chord has frequencies of (1, 5/4, 3/2) with a gcd of 1/4, another octave lower. A minor chord has (1, 6/5, 3/2) with a gcd of 1/10 which does not work all that well, but if you look for the minor third in the overtone series, you get something closer to (1, 19/16, 3/2) which puts you at 1/16.
So for major chords, but much more so for minor ones, the "insinuated" root note is much lower than for power chords, and if you start from a low note already, the insinuated root note will be outside of hearing range and more like a low-frequency vibration/oscillation. This "insinuation" is not purely virtual: it is the actual periodicity of the resulting full signal and any sympathetic low-frequency vibration will occur with it or one of its overtones.
If it is outside the range of normal hearing, it will not be perceived as contributing to harmony since it does not register in a fixed position in the inner ear (which is the ultimate instance of sympathetic vibration involved in hearing).
In addition, many instruments have "disharmonicity" increasingly in lower notes, meaning that the physical overtones are not whole multiples of the fundamentals. String instruments with thick strings in comparison to their length (particularly smaller/upright pianos but also the low notes of a viola, comparatively short strings for their range, and smaller double basses and clean(!) electric basses), wind pipes with significant end effects and a few others.
Contrast this to instruments with a high-overtone harmonic oscillator (vocal chords, brass and reed instruments as well as free-reeds like harmonium, accordion, reed organ): here the overtones are forced to be a multiple of the fundamental because of a regularly stopped air stream. Working with them as material tends to produce somewhat less muddy harmonic stacking, but they still have the problem of an implied fundamental possibly getting out of hearing range.
Also their high overtone content, harmonic or not, makes them most eligible for power-of-two implications. So the difference in workability at low pitch for major and minor chords gets even worse than with low-overtone bass instruments.
With any chord, you want to define it as efficiently and with as much clarity as possible (i'm writing this from a jazz piano background, so this may or may not be a good explanation)
First off, defining the root note - it's going to get muddy down there if the root isn't way down there on its own. Think of what a bass player is doing - they're not playing big thick chords, because it would sound like a big cluster of mud if they did. Yep, it is due to harmonics, or overtones. Way down that low, there's way too many first, second and third harmonics clashing if multiple notes played - our ear can't make it out, and it becomes noise pretty quickly without definition.
On the other hand, think of a big clear root note, with a third defining the chord an octave or two above that, with a seven and nine shimmering over the top. It's big, it's open, it's simple, it breathes, and we can differentiate every note of the chord, rather than having all those notes fighting each other for space