Empirically, this does not seem to be the case. Labov at UPenn has been studying American dialect formation for the past ~50 years, and has found several ongoing changes. In some ways the Midwest is getting more divergent, with the Northern Cities Vowel Shift.
Many small dialects are disappearing, but others are becoming more divergent (out west). It's a mixed bag.
Many small dialects are disappearing, but others are becoming more divergent (out west). It's a mixed bag.