I'd say Super Mario Sunshine's reputation as the worst 3D Mario is deserved. But that doesn't mean it's a bad game. Something HAS to be the worst 3D Mario. It's a credit to Nintendo that the worst game in that series would probably be a high mark in other series.
I find that F.L.U.D.D feels rather forced and it hurts the game. At the time Nintendo had a very impressive reputation for innovation and creativity. They had taken almost all of their franchises from 2D to 3D and had pulled it off every time, usually with ground-breaking games that influenced the entire industry. Such a reputation can be hard to live up to. I find on the Gamecube, particularly with sequels, Nintendo suddenly found themselves with writer's block at the worst time. This Mario game had to be bigger and better than the games that came before it and had to change the industry. It could not just be a better polished take on Super Mario 64 because, dammit, Mario doesn't rest on its laurels like that! F.L.U.D.D. was their innovative new idea that was supposed to make Sunshine unique and essential. Hell they made out like it was some big top secret idea that everyone would copy. They were probably hoping people would copy it because then it was the industry changing idea they needed it to be. It wasn't. Nintendo did this again with Mario Kart: Double Dash. The double karts are the major unique element of that game but it also feels forced and like F.L.U.D.D. did not influence other games or appear again in later sequels.
I think it demonstrates the importance of creating new IP on a regular basis. Early on in a series ideas for a sequel can be obvious as you can work in ideas that were left on the cutting room floor of the original game or address shortcomings in the earlier games. But over time it becomes harder and harder to keep the originality up while keeping true to the general gameplay of the series that made it popular in the first place. For every series there will come a time where the ideas just aren't there.
Nintendo started to hit that point on the Gamecube, which made sense because many of their franchises were clocking over 15 years at that point. There was no such issues with games like Pikmin, which was brand new, or Metroid Prime, which did the switch to 3D that gave so many Nintendo franchises new life on the N64. I think Nintendo has had trouble coming to terms with this as they've since become infatuated with gimmick control schemes, hoping in vain that such gimmicks will inspire new ideas. Once they tried waterpacks, today they try tablet controllers.
What's interesting is that Mario bounced back. Super Mario Galaxy felt legitimately innovative, not forced. Nintendo also came up with a new take on 3D Mario with Super Mario 3D Land. Sometimes the new idea is just not there today and will come tomorrow. If Nintendo felt confident enough to take a break from their established series when the inspiration isn't there they wouldn't have to feel that gimmicks are necessary or that they need to force in some half-baked concept that doesn't gel. There is a massive difference between sitting down and thinking "what game ideas do we have that we can develop on?" and "okay I've got to make a new Mario/Zelda/Metroid/Pokémon game for this timeframe so what ideas can I think of for that?"