With EADGCF tuning, barre chords wouldn't work so well, since the top and bottom strings would be a half-step apart (disregarding octaves) creating dissonance. Or rather, EADGBE tuning works well with barre chords because the top and bottom strings are the same note. An open-chord tuning works even better with barre chords, but only for that one chord shape. EADGBE gained predominance partly because it strikes an uneasy compromise between different chord shapes and barre-chord friendliness.