RMSE in Bayesian Context

When accessing model fit, it seems like a lot of people have been using existing packages in R or Python.

However, with a package, we are simply getting the traditional RMSE as:

In the Bayesian context where we have posterior samples from each prediction of interest, we can express this equation as:

I know there's now a `m.predictive_samples(future)` function built into v0.2 so this wouldn't be hard to add. What are people thoughts? It seems like we are losing a lot of the uncertainty we gain from fitting a Bayesian model by simply using the posterior mean for model fit evaluation.