Incidentally, the reason that the open C chord with the Low E seems difficult has nothing to do with the intonation of the third--it has to do with the fact that the interval between the Low E and C on the A string is a Augmented 5th--

Low E to B on the A string(second fret), is a perfect 5th-move up one half-step to C and you will hear a very striking dissonance--

That dissonant augmented fifth sound is part of part of every major chord--whether you've studied music theory, and know it's there, or whether you are like Mysha, and think that technical terms are only for "professionals"--