These used to be corrals for keeping livestock penned up at night, when the desert was grassland (not that long ago, as some have pointed out).
Over the years, most of the stone was stolen to make other structures, except for the lowest layers that were underground at that time. Now it's desert and the topsoil has blown away, leaving a low wall.
Your theory makes sense.
Good hypothesis. I guess my quesion would then be “where are these other newer stone structures?” I suppose the answer is that they would be under a mountain of sand somewhere. Seems like there are none in this vast lava field so they came to take the rocks and move them to some vast distance. Except these aren’t some specially quarried rocks, they’re just a bunch of rough rocks like you’d find anywhere. so why bother lugging them to who knows where?