> Now that we can have electronic instruments that "tune" themselves, could we compute song-optimal tunings that preserve the intervals used most in that song?

We've had self-tuning instruments for thousands of years. Vocal harmony has almost always been perfectly tuned for its key. Likewise orchestral strings are fretless and can produce perfect intervals. Equitemperment was an innovation in the 17th century because it approximated the perfect intervals very well ("sounded good") but also permitted the ability to simultaneously represent scales based on every note in the circle of fifths ("sounded interesting"). But the "real" chords were always (well, since the late middle ages) understood to be integer ratios.