The reason I have not implemented the approach you suggest is because I believe it is not statistically fully appropriate. Specifically, the Mauchly test, as any significance test, has a specific power and Type I error rate (the latter of which is controlled by the alpha/significance level). I do not believe it is worthwhile to incorporate these additional error probabilities into an analysis. Instead, I believe that the small loss in power by always using Greenhouse-Geisser is overall a more appropriate strategy and more conservative.
Consider the case in which the Mauchly test fails to correctly detect a violation because the power is too low in a specific case. If this happens, you get inflated Type I error rates. I consider this a potentially larger drawback than occasionally committing a Type II error in case Greenhouse-Geisser is too strict.
I believe that in general, significance tests for testing assumptions is not a good idea. For some arguments why see:
Nevertheless, the current development version of
afex now makes it easier to get assumption tests, see: