There is increasing momentum surrounding the hypothesis that rates of molecular evolution between individuals within contemporary populations are high, and that these rates decrease as a function of time, perhaps over several millions of years, before reaching stationarity. The implications of this are powerful, potentially reshaping our view of how climate history impacts upon both species distribution patterns and the geographic structuring of genetic variation within species. However, our assessment of the hypothesis reveals a lack of theoretical support and empirical evidence for hypothesized magnitudes of time‐dependent rates of molecular evolution, with much of the apparent rate changes coming from artefacts and biases inherent in the methods of rate estimation. Our assessment also reveals a problem with how serial sampling is implemented for mutation rate estimation using ancient DNA samples, rendering published estimates unreliable.