Taylor has absolutely no reason to do it. What would she gain? Her singles and albums sell like hotcakes, and her concerts sell out in minutes. There's no money to be had because the NFL has recently flipped the model and requires the performer to pay them. The Super Bowl halftime spot can't help her at all.
If nothing else, it would give her a significant PR bump. The general reaction to her last single & her persona over the last year has been pretty negative - and a Super Bowl Halftime show would basically serve as a massive advertisement for her personal brand. Which I agree, she doesn't really need. But it could be a smart pre-emptive strike against future backlash - just by reminding people that she's still a killer performer.
Plus, imagine burying the hatchet by bringing Perry or Kanye on stage for a collaboration. That's the kind of moment that can rewrite a narrative.