So this business of the existence of points in spacetime. Physics works just fine when it treats the earth and moon as "pointlike", it's a matter of scale after all. A point is a thing Newton says must exist at the centre of any massive object, the physics is based on this idea. But the idea is classical, or, more or less, based on anthropocentric "intervals" of time. As these intervals get smaller, the universe gets less and less classical--but Newton didn't know that.