I'll add this to what you say -
How can there be a day of zero work to exclusively worship? To elaborate, here are a few brief examples -
Changing a babies diaper is work, taking your dog out to be pee is "work", so is cleaning the tub after a bath. ETC., ETC. Those are things that must be done, even on a Holy day of rest. I know this is awfully bare bones literal but this is what I wonder.