>Saying that a gravitational field has no entropy is just incorrect.

The thermodynamic definition of entropy is the energy that is wasted, that is the energy that does not accomplish any work per se. Saying that gravity in a system that does not have an event horizon, as in a normal star, must have entropy is not necessarily correct. As gravity is a very weak force it may very well have no entropy (wasted energy) in a system that has no event horizon (black holes have event horizons other celestial bodies do not).

You are quite correct is saying that some very important advances in the understanding of gravity is the arena of quantom field theories in the recent times have been accomplished.