The discussion in the gemarra (kesuvos 11a) revolves around the kesuba given to a katana who was converted as a child [and got married before she became a Gedolah].
It she is a gioress she has no halachic father or brother. Who then could marry her off as a katana?
In Even ha'Ezer 155 the majority view is that a Ketanah can marry herself off after age six, based on the Girsa of the Rif and Rambam in Gitin 65a. However according to the minority view your point is valid.
See our Insights to Yevamos 107:1:a, where we quoted the TZAFNAS PANE'ACH (Hilchos Ishus 4:7) who cites Rashi in Gitin (65a, DH u'Chenegdan), and in Kidushin (44b, DH Ma'aseh Yesomah) that says explicitly that a Ketanah can be Mekadesh herself -- at least when she is a "Yesomah" (even a Yesomah b'Chayei ha'Av). This seems clear from Yevamos 108a also, where it discusses a Ketanah who "accepts [on her own] a Kidushin."