You can absolutely sing a perfect chord. That's most of the idea behind styles like barbershop, for example. But things start to fall apart when chords transition between each other. The first and third notes of the central chords in a key will line up on top of each other, but the middle notes of the chords and triads based on other notes don't. So just like an equitempered scale sounds a tiny bit off, harmony gets wonky too if you try to do interesting things.
So the compromise we've all settled on is that we play music in the equitempered scale, and only adjust a little bit here and there to exploit perfect tunings in limited, style-dependent ways.
Which is to say: perfect chords are interesting flavor, but at the end of the day kinda boring in isolation; "real" music needs more rules.
Awesome appreciate you explaining this. Hadn't considered the idea that transitions vs simultaneous notes "compete" on what the optimal note frequencies are. And very cool to understand that people are dealing with this pragmatically all the time.
So the compromise we've all settled on is that we play music in the equitempered scale, and only adjust a little bit here and there to exploit perfect tunings in limited, style-dependent ways.
Which is to say: perfect chords are interesting flavor, but at the end of the day kinda boring in isolation; "real" music needs more rules.