Boss refights would probably come later, after the Main Story. And I'd do it in a manner similar to the "Boss Endurance" mode in Kirby's Adventure/Nightmare in Dream Land that I could never beat when I was a kid. (I always choked at Meta Knight or Dedede.)
You still get the same Tower Points, and the rewards upstairs will update accordingly, but there also might be some unique rewards in this challenge depending on different "high scores" in the challenge. I'll have to think about it!