Maybe "indeterminate pitch"? The Beatles piece "A Day in the Life" has one or two passages where the orchestra is instructed to glide from one pitch to another individually. It seems to fit your description. Since we are talking here about mainstream pop music, "avantgarde" or "atonal" is not really a fitting label, and "unpitched" also does not fit the bill as we are just talking unsynchronized pitched instruments.
Of course, your example of 4'33" trivially meets the label "unpitched". And so does a number of purely percussive pieces (note that some percussive instruments have determinate pitch as well, like timpani and cowbells, and some are used melodically, like tubular bells, marimba, glockenspiel, xylophone, celesta...).
So generally your description covers a rather large body of music, large enough that it would probably be a bit difficult to subsume all of it under a single label.