As others have discussed, the need to marginalize over continuous predictors makes implementation challenging. Estimating the joint distribution of the predictors is also a big problem:
The Mahalanobis distance is appropriate when the joint distribution is multivariate normal, but such a distribution is unlikely for many predictors (perhaps this is arguable).
The joint distribution of the predictors in the experiment may not reflect the joint distribution of the predictors in the “real world”. For example, an experiment might pair certain temperature treatments with different humidity treatments, but those temperature-humidity pairings may be unlikely in the real world. Hence, conclusions based on the joint distribution in the experiment may not be meaningful outside the context of the experiment.