A few things:
-Yes, equal temperament exists and can be considered a compromise. When we use frets we are almost completely bound by it.
-Even accurately placed frets are not perfect because of string gauge and tension differences. It may not even be possible to have perfect intonation at all frets with only one string, and it is definitely impossible (with normal frets) with more than one string.
-Ideally, the 12th fret note will be an exact octave of the open string, but there is nothing magical about that. If you play the 7th fret (for example) more than the 12th fret, why not set the intonation so it is correct at the 7th fret and allow a slight error at the 12th rather than the other way around?
-Electronic tuners don't care what note you start with if you use the tuner for all strings. If, like I do, you tune one string (I use a tuning fork) and then tune the rest of the strings to that, there may end up being slight differences depending on what string you start with, but any differences will be very slight is they exist at all.
-Tuning is and will always be a compromise. The best we can do is reduce errors to a minimum through string gauge choices, good fret work, and adjustments at the bridge and nut, and then accept the inevitable errors. We can move errors to more suitable areas of the fingerboard so that we can play more 'in tune', and we can tune the instrument specifically for certain songs or tunes to improve intonation.
One of my favorite guitarists that I've have heard play live is Martin Simpson. He plays in various different tunings in the course of a show, and changing tunings is something that throws all of our careful bridge and nut 'compensating' out the window. As he would talk to the audience between tunes he would re-tune his guitar by ear, often repeatedly playing a figure and adjusting the tuning. During the next tune or song, especially when he would sustain a chord or a note or two, the guitar would ring out so exactly in tune that it made a definite impression on me. He did that by tuning the guitar so that errors fell somewhere other than the frets where he needed the intonation to be good for that song, all the while speaking to the audience to spin a web and draw them into the song. A masterful entertainer for sure, but a big part of that was his technical ability to tune his guitar.
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