Cary, some of your objections to squares seem a bit contradictory. Let me re-state them, and see if I've understood you correctly.
Some squares are unphrased, and those squares have less opportunity to connect your movement to the music.
Many squares are danced for a shorter time than contradances are usually danced, and therefore take relatively longer to teach compared to the dancing time.
Many squares are mixers, and therefore have less time dancing with your original partner than in a contra.
Some squares have visiting couple dances, in which the dancers can only make movements in place during some of the music.