On the contrary, this is best description of what conservation of energy means: all externally generated forces acting on the system do vary with time. Im other words, this is a closed system as defined in thermodynamics.
The nature of energy is really just a result of this property.
The difficulties with energy in GR are related to the fact that those equations alone allow for space-times that are truly bizarre. Some that are technically solutions to the field equations are clearly nonphysical (e.g. Goedel's solutions). There is also a priori no reason why e.g. expanding metrics should actually yield proper conservation of energy.
The nature of energy is really just a result of this property.
The difficulties with energy in GR are related to the fact that those equations alone allow for space-times that are truly bizarre. Some that are technically solutions to the field equations are clearly nonphysical (e.g. Goedel's solutions). There is also a priori no reason why e.g. expanding metrics should actually yield proper conservation of energy.