Wikipedia is not a genealogy site, so wouldn't typically cite a source for the name. Werelate may not have the functionality to cite the name. Or because so many people don't cite the name. Just because it's not done doesn't mean it shouldn't be done. ;-)
While, yes, you could use a cited birth or marriage date to support evidence for the name and relationship (to parents, children, spouse), sometimes a vital record does not exist or hasn't been found.
For example, a person's will may identify her children by name, but no birth dates are included. Therefore, you'd cite the will as proof that John Smith was the son of Mary Jones Smith. And the place to do that would be the name of John Smith.
And technically (I think I'm channeling Elizabeth Shown Mills here), when you cite a birth date, you're providing evidence for the DATE (and perhaps place) NOT for the name. Mills would argue that you need to cite both the NAME and the DATE, separately.
And in the example you provide above, it looks like whoever uploaded the GEDCOM *did* provide a source for the name. A crappy one, but a source nonetheless. In the absence of a better source, it should be retained.