It might interesting to think about why documents don't have to be signed with the same characters or style as the driver license. By characters, I mean the exact letters of the alphabet and punctuation marks the signature is meant to represent, regardless of whether the signature is easy, hard, or impossible to read. By style, I mean how the signature looks: neat, messy, lots of loops, mostly straight lines, etc.
Each state has a bunch of rules about how to prove to the DMV that a certain name belongs to the driver, and what characters can appear in the name. Depending on when the license was issued and the technology a state uses, there may be a limit on how many characters are allowed, whether accented letters like Ä are allowed, whether dashes and apostrophes are allowed, etc.
The style of the signature on the license may be affected by using an electronic pen, which often just don't write the same way as an ink pen.
I've never seen a rule that says the name or signature from the license has to be used in any other sphere of activity, except that sometimes there's a rule that the name you use for some activities must match the name on the ID you presented when you registered to begin the activity. But you always have the option to prove your identity in a variety of ways, such as passport, military ID, sometimes birth certificate, etc. When I filed my oath of office to become a notary, I was IDed by the personal knowledge of the town clerk who administered my solemn affirmation.
Also consider a person who has injured her writing hand, and has to sign with her non-dominant hand. Does that mean she can't sell her house the day after the injury? Of course not.