A simple experiment

Tune the open strings carefully with a tuner. The open strings are now correctly tuned to equal temperament.

When you try different chords using open strings, some will sound all right while others will sound considerably worse. The thicker the strings, the more problems you will encounter. Presumably you can't accept it, so you try to adjust the tuning until the chords will sound acceptable.

Are you familiar with this situation? Even though you know that the open strings are correctly tuned, you tinker with the tuning! You are far from equal temperament.

Put a capo on the first or second fret and tune the open strings carefully with the tuner. You will now experience a radical improvement. The chords will intonate much better. Not 100 %, but quite a lot better.

What happened? The faults in the nut were eliminated by the capo! The faults in the bridge remain, but the result is a lot better. You have now come about halfway to equal temperament.

Can you imagine what it would be like if the faults in the bridge were eliminated? That each string was individually compensated at the bridge to note correctly. If you have an electric guitar you can easily try. Keep the capo on. In the usual manner adjust the length of the strings at the bridge, so that the octaves are in unison with the harmonics at the middle of the strings.

You will experience another radical improvement and now you have actually reached the goal. You can play anything and everything you do sounds perfect. There is nothing false. Your guitar is almost perfectly in tune with equal temperament! I say "almost" because there is a tiny fault added by the capo. The result also depends on how accurate your tuner is. But you have come close. You have got a taste of how it is to play on a perfectly intonated instrument.

Notice how the tone improves. The notes will sing high up the neck even with thick, old strings on an acoustic instrument. The explanation is that the tone of an instrument to a very large extent depends on the resonating overtones in the strings you are not playing upon! The better the instrument is intonated, the easier the overtones will resonate.

Unfortunately, as soon you remove the capo it is destroyed. It will sound perfect as long as you fret the strings, but the open strings will sound false. When you tune the open strings all other notes will be out of tune. Sorry!