I think the 'CROX' thing is a choice most of the time. I personally would file it under the 'CHOICES.' category (see also: Open Your Heart performance at the Grammys with the group gay wedding thing; the grillz; Drake Coachella performance; heavily autotuning her vocals etc.) Obviously sometimes it's poor technique but a lot of the time I think she actually chooses to sing that way.
As for the heavy backing tracks in this performance, I kind of understand why she did it. It's the first unveiling of a brand new song after she's been away for a long time. It's live television, and last time she did something this big, something went hugely wrong. So I guess she wanted to play it a bit safe. Her mic was on anyway and she was singing off and on throughout the song.
I also don't think it's fair to compare one-off live performances at award shows when she's coming off a period of quietude to when she's on tour as she clearly gets her vocal coaching in check before she goes on tour as part of the long rehearsal process. And don't forget that a lot of the time when she sounds great on tour is when she's sat down and concentrating on the vocals not when she's running around on stage doing choreography ....