A statistical model should be rejected if it fails a posteriori goodness-of-fit diagnostics.

That is, the observed distribution of model error (residuals), once the model has been fit to the data, must be consistent with the model error distribution as initially specified.

A statistical model is not an acceptable model just because P-values for the parameters are significantly different from a particular null value at some chosen alpha.

The quality of a statistical model fit is judged by its diagnostics, not by the P-values of the parameter estimates!

Goodness-of-fit schemes can be a complex and time-consuming (on a computer) aspect of model fitting.

The highest quality diagnostics can require parametric bootstrapping, hence the need to code the forward (simulation) model as well as the inverse (estimation) model.

A statistical model that has not passed goodness-of-fit diagnostics should not be accepted nor trusted.

Goodness-of-fit testing is not an incidental nor trivial aspect of statistical model estimation and inference.