The back foot lifting prematurely can be an indicator of some other issue in the delivery. For example, posture or early shoulder rotation issues often cause the back foot to lift prematurely. In these cases, fixing the issue will usually restore the natural back foot drag.
However, there can be cases where a pitcher has trouble fixing the underlying issue so having the pitcher deliberately drag the back foot can help. (I’ve seen Tom House do this effectively with a pitcher.) Yes, the pitcher will likely slow down as deliberately dragging the back foot will be rather awkward. But he should be able to stop the deliberate drag once he works through the issues and should then be able to speed back up.
Keep in mind that some pitchers just don’t drag their back foot. Curt Schilling was probably the poster boy for lifting the back foot.