I excluded cephalopods by restricting my blueskying to chordates. But they do have a body plan, the simplest of all: A tube, aka an extruded torus. That must've been the precursor for later more complex body plans...except that, topologically, every body plan is a torus, everything else is detail. What every damn animal phylum has in common is that the food goes in one end and the waste comes out the other.

Such is the Essence of Life.

Insects are segmented, and individual segments exhibit bilateral symmetry and two or four limbs (four when the segment supports wings). Other animals, like centipedes, I think of as "serially bipedal" (google "human centipede" at your own peril; it's even less appetizing than googling "santorum"). Bottom line: Insects aren't really a different body plan, they just have a replicated body plan.