s/those 4000/another extremely diverse 4000/
you are making a massive assumption that we prefer the same old same old. Some of us are always on the lookout for a bit of strange
Pythagorean tuning makes a ton of sense if you’re trying to tune a fretted stringed instrument (and haven’t tried playing anything with a key change), but it’s an oversimplification of how music works. The Pythagorean philosophical mistake is treating the tuning system as a theory of music itself, when it’s really a simple framework for certain types of music.
That's quite the claim, do you have anything to support it beyond your intuition?
Musical perception shares pathways with speech and it is believed this is also why certain timbres seem more expressive or interesting to us than others (that's over my head, but I first encountered that claim in the teaching company lecture series on mathematics and music). Let's consider that the first music must have been vocal or percussive, and that music making is innate to humans. Let's also consider that our hearing has to be able to finely distinguish sounds in the frequency range our voices can produce. This is why we don't make musical instruments only cats and dogs can hear at the very least -- our musical instruments have significant overlap with not only the sounds we can hear, but especially those we can produce vocally.
In terms of Western music, earliest polyphony was vocal. Contrapuntal technique likewise arose from vocal music (and this yielded our common practice harmonic tradition). I think every counterpoint manual since the renaissance (at least the ones I've read from Zarlino to Fux) begins with a discussion of the idiophone to establish the concepts of consonances and disonances based on proportions and then abruptly gets on with the business of counterpoint, where the ideal of the voice is mentioned whenever instrumental music is brought up. Additionally, there are special cases in counterpoint that arise from (or are explained as having arisen from) the sort of embellishments vocalist were fond of making (e.g. nota cambiata for one example). Not to beat a dead horse, but I even recall reading a fugue manual from the 1700s discussing an instrumental fugue and pointing out that the first note of the subject is longer, being a mannerism from vocal fugue writing (singers felt more secure if they could sit on the note a little at the beginning of an entrance).
Every single manual I've read on instrumental performance has stressed achieving a vocal quality. This is really deeply baked into Western music.
A) Most people wouldn't be able to tune an instrument like what you describe accurately enough to contradict the result. Practically all the intervals would be slightly off, and
B) The result really does contradict Pythagoras, who postulated that musical beauty arose from the mathematical perfection of those ratios. Contradicting Pythagoras in this is, of course, hardly new. More interesting is the idea that there may be entirely new forms of naturally appealing harmony out there to explore.
This is why many subtractive synthesizers have a detune parameter, to slightly offset oscillators that are nominally tuned to the same frequency. Chorus, phasers, and flangers are similarly used to add texture and color to sounds by using slight frequency or phase delays to create interference signals that make the sound 'move' and make it sound larger and more distinct.
When slightly detuned, it's so close to the perfect ratio that it still satisfies our preference for perfect ratios, and it also fills more of the frequency spectrum (which is another thing we like).