It's not exactly equal temperment that is to blame. It's the fact that a modern steel string guitar is the result of a design history that is not completely compatible with equal temperment.
There are two main factors at work. First, the way a guitar works is based on the idea that one fret position can create the right fundamental frequency for six different strings. Now this is true enough that people make and enjoy all kinds of music with guitars all the time, and have done so for over 100 years. But it's not actually 100% accurate. As our ears develop as musicians we can start to detect the inaccuracies of the fret positions and it can annoy us more and more, no matter how much we adjust the intonation set at the bridge or play around with different string gauges.
The second factor is that a long time ago, acoustic guitars were strung with gut, not steel, and jigs and templates for necks, bridge position, and most importantly fret positions were created for gut strings. Then when steel string guitars were developed, those jigs and templates were not always adjusted to match the radically different string thickness and stiffness of steel strings. Some of those fret position calculations, jigs, and templates have persisted to this day. That means a lot of nuts are positioned too far from the first fret, even on guitars from major manufacturers.
Combine that with the desire to make sure a new guitar doesn't buzz no matter how hard it's played, which means you need to cut the nut slots pretty shallow, and you create major intonation problems for the open chords (including the cowboy chords) on many steel string guitars that are fresh from the factory.
Some "quick" fixes are to cut the nut slots down a bit (at least for players who have a more appropriate touch) and even to move the nut about 1/32" to 1/16" closer to the first fret, which has the heart-stopping requirement of permanently removing a sliver of the fingerboard.
A more sophisticated fix is to have a compensated nut (e.g., Earvana, Buzz Feiten, etc.) professionally installed.
All of these things help (and there are many other options out there instead of or in addition to these!), but there is no solution to the problem. The guitar will always be an approximation of equal temperment. One thing that I believe makes the guitar a compelling instrument for people to play and hear is the very fact that it's "wrong". It has a subtle rebellious quality. It sometimes sounds a little close to just intonation, other times it's an approximation of equal temperment, and most of the time it's just a bit inharmonic everywhere. I think people have learned to like it that way.