@Bigtop: She also performed in
2012, it had some backlash because of the vocals (which were pretty bad anyway).
Last year she did it again, but it was better. She sounds fine right now, good enough for live tv.
As far as I know, the most backlash she ever had for a performance was the
Best Artist 2009, which she even apologize saying it was her "personal worst" (for a TV performance, yes it was, but CDL 2007-2008 still haunts me).
I'm sure it's not a problem of her being invited for those shows, she probably doesn't want to do them anymore. The same goes for Namie and Kumi. Even Music Station lately is all about girlgroups and boybands.