I just finished Bowser's Fury with 77 out of the 100 Cat Shines, which is the best it seems I could have done before accessing the post-game content.
Bowser's Fury is neat. It's an interesting combination of 3D World & Odyssey, but I don't feel like the timer element of Fury Bowser adds much to the experience other than annoyance. So many times I got those Cat Shines either JUST before he appeared or during his invulnerability period at the tail end of his appearance, so they essentially "didn't count" in dealing damage. Ran into some issues getting his fire breath to hit the Fury Blocks on occasion, too.
I think I would have rather had him just be a recurring boss between the blocks of islands rather than a frequent annoyance capped off by middling boss fights with a wonky camera.
From what I've gathered, he doesn't "turn off" in the post-game once he spawns, so the only way TO send him back is with Cat Shines. I guess he'll be an actual threat in the post-game, then, because the main game is pretty easy?
Edit: Completed 100%. The cosmetic reward you get...really isn't worth it, but at least the final fight with Bowser is more interesting once you have 100 Cat Shines by virtue of Bowser having a different look & a full health bar.