Another singer who I really like, who also used to sound bad in live televised performances is Kelly Clarkson. But lately, her live televised performances have been great. I remember around 2003 or so telling my parents how great Kelly is, and then they heard a live televised performance, and said "all she does is scream" and "she sounds like a cat getting its tail stepped on, except a cat would sound more melodic". In more recent performances, they liked her, and I'm not sure if they even realize she's the same person. It seems that is happening with Katy now. Since Kelly and Katy are both the type who stand up for themselves and do not allow anyone (especially record company executives) to bully them around (perhaps why I like both of them so much), were the executives sabotaging their performances, since they refused to be doormats? Or are these performances a skill that Kelly eventually learned, that Katy can still learn?
I still say that Katy should cancel if she's feeling sick and it affects her voice. Any subpar performance, no matter how good her reason is, is just going to give more ammunition to the people who insist she "can't sing live".