As I am learning to use a straight I am slowly starting to learn how important it is to stretch the when there is no safety bar.
But, with the DE, I still feel that it is better to not stretch the skin too much. There doesn't seem to be a need, maybe the safety bar stretches the skin before the blade just a little. Moreover, with the ATG pass on a DE, I get irritation if my skin is too taught - even without stretching by hand. On a practical side too, since you only use one hand (usually) to use a DE, it is tough to stretch the skin over the whole face.
Razors don't shave people. People shave people!
There are three critical types of moments in life: Times when we should use opportunity to be enamoured with finer details, and times we should ignore the minutia.