Rests are not quite redundant. Imagine a piece written in 4/4 that has only two quarter notes in a particular measure. Rests are necessary to indicate exactly when the quarter notes are to be played. Example: compare Q R R Q (Q=quarter note, R=quarter rest) with Q Q R R, or R Q R Q, or Q Q (i.e. no rests indicated). They are all different (the last one is entirely wrong). The rule simply is that a measure must contain the correct number of beats made up of notes and rests.
Having said that, in pieces with more than one voice, one often finds that rests are omitted for the second, third, etc. voice(s). This is OK, as long as the notes for the other voices are aligned with the notes from the first voice, so it is clear when to play them.