That’s my point though. The moon hasn’t degraded and crashed into the earth so it’s clearly possible for a satellite to orbit the earth indefinitely - for some suitable definition of indefinite.

The moon’s orbit is taking it further from Earth over time, it it’s very far away and very massive, as well as being influenced by the Sun. A satellite’s mass is almost negligible, and compared to the Earth-Moon distance it’s distance from Earth is too. A pebble hitting the moon also isn’t going to do much to change its course, while the same pebble will do a lot more to a satellite. The same is true of dust.

The moon has a ton of mass and—therefore—inertia. The chaotic effects of the system are still present, but require dramatically larger timescales to notice any kind of effect.

The moon's stability is a good point, but not conclusive. The moon's orbit isn't perturbed by it's own gravity. It's also much larger, so much more mass (radius cubed)/surface area (radius squared), so less affected by solar wind, micro meteor impacts, and the like.

But still, it's more likely we'd find evidence of a distant past civilisation on the moon than on earth right?