As a first (or zeroeth) order approximation, we might treat the Earth or Moon as point masses (just as with the aluminum ball). Is that author seriously claiming that Einstein was ignorant of tidal forces?
The Earth and Moon would not necessarily have equivalent acceleration in an Einsteinian universe any more than a Newtownian universe. Whether it's sufficient to think of them as point masses depends on the distances involved and the precision required.
Why would we use a point mass approximation? Because it's easier and quicker to compute. We don't need a computer simulation to get good results. Also, even in a computer, the actual situation being modeled might be so computation intensive that a mesh (or other) simulation might be impractical. OR, it could be that a hybrid simulation is in order where some things are modeled at low resolution (point mass) and others high (solid with fine mesh).
It's not a limitation of Einstein. Scientists try to use the simplest math they can get away with.
