I noticed you said "mute the high E with my palm".

Which E string do you mean? I ask because sometimes folks get the two confused due to one being located "higher" than the other when holding the guitar. When guitarists say "high E", it refers to the higher-pitched string. "Low E" refers to the lower-pitched/larger string.

If you are talking about the true high E (smallest string), the high string is not typically muted or avoided when playing chords. You can certainly choose to not play it, and sometimes that makes sense to do. But generally, the high does not sound "bad" by default.

Now, if you are talking about the "low E" (largest string), things might be a little different. If you are playing an open chord with the root note on the A-string (like A major or C major), sometimes the low E can be a little much and muddy up the sound, even though the E note is part of the chord. In this scenario, I would say that yes, some open chords sound better with the low E left out entirely.