This is more of what I was getting at; back when she was first up-and-coming and becoming a clear contender. Not x amount of albums and globally sold-out shows later. And to the sibling comment's point, I do actually think she's less influential than she has been in the past.
Is she influential? I think she's Dale Bozzio: The Next Generation down to the fashion (since who the fuck remembers the 80s, right?) with a bit of Madonna and Gwen Stefani along the way. In another fifteen years we'll see someone else doing the same schtick and most people will not remember any previous iteration of it.
She seems to have pretty well dropped off the radar in the second half of 2012. I'm hard-pressed to think of any very culturally influential rising stars in female pop--the standouts seem to be on flat or downward trajectories.