The main take away for a lay person is that _like_ the mattress space is being deformed. That's where the analogy stops. Taking it further, like with all analogies, breaks the analogy.

If the analogy was a perfect one, then it would just be the reason and not an analogy.

My main gripe is how hard for most people it is to extrapolate that deformed mattress into a 3d space.

They use that to explain why you don't feel acceleration when you jump off a building or out of a plane.

They say you DO feel it when you are standing, because the earth is impeding you and pushing you away from the geodesic you naturally want to follow.

So it is counterintuitive. the standing still person is being accelerated/pushed. The freefall person is free.

John wheeler said "Spacetime tells matter how to move; matter tells spacetime how to curve". I think it explains the circular nature.

Mass curves spacetime, that changes how mass moves , mass moving to a new position changes the curvature, that changes how the mass will move next. The dimple in the mattress staying with the mass.