The purpose of the reduced model
The two main uses for reduced models are for simulation (to simulate new scenarios and for design) or estimation (to be used in software like NONMEM for estimating parameters for new populations).
For simulation, any method can be used if the simulation is based on sets of input variables (e.g. doses, dose intervals, observation times) that were considered when the model reduction was conducted. For instance, if pseudo-data were simulated from the full-order model to develop a reduced model then the reduced model can only be used to interpolate within the range of pseudo-data inputs. In contrast, any fully parametric method, can be used to simulate under (in theory) any set of input variables. In this context, semiparametric methods such as balanced truncation behave like nonparametric methods.
However, if the purpose of the reduced model is to be used for estimation then any fully parametric method could be used for model-order reduction. The utility of the Empirical Approximation will depend on the circumstance. Importantly, though if it was desirable for the parameters to provide some mechanistic meaning then only the fully parametric methods would be of value.