That is not something inherent in guitars themselves, it is the norm in steel string guitars and the fan-braced/Spanish guitar but mostly because that is the norm for all those mass produced guitars which make up the bulk of guitars. On steel string you can often greatly decrease this quality just by switching to flatwounds, this is part of the flatwound sound, it shifts the timbrel content into the players technique but if you want much timbrel content with flatwounds you need heavy strings and a high action, and the hand strength and technique that sort of setup requires.

Before the rise of the steel string and the Spanish guitar, guitars tended to be more even across their range and also had less bass which helped even them out, and now that sound is what we are used to. There have always been niches that wanted that more even sound, but for most that just makes it more difficult to play all that music that developed around these quirks, so they remain niches.

I'm not doing fancy AI stuff but I have worked a lot with my own bespoke supercollider system where I record whole fretboards of guitars and then play alternative notes based off of certain rules. For whatever dumb reason though, the most natural sounding thing is really just playing, e.g., any random D4 from its possibilities at any given moment.

Timbral differences also exist depending on force, the manner plucked, the already ringing overtones... It's hard to know what you want, but the most natural thing is always going to be some organic variation in the notes in general.

If you have a good ear, you aren't, I don't think, hearing so much the timbral diff in the individual open or fretted notes as much as the fact that a barre chord and an open chord is a different voicing of the same harmony.