I wouldn't call adding the trio gimmick, making players replay the exact same levels with slight differences 4 times instead of having varied campaigns and objectives for each character, and giving enemies (that took one hit to kill in previous games) huge healthbars to justify new unnecessary combat mechanics "cutting the fat". Like I said, they're just similar to the Sonic/Shadow stages, not actually a proper evolution of them.
As for the story, let me put it simply. In Adventure 2, Sonic doesn't just appear in Metal Harbor for the heck of it, he's there because he broke out of the base's prison after being caught in City Escape. Then he goes to Green Forest because Shadow is there trying to find the Chaos Emeralds, and so on. You couldn't really rearrange the level order of SA2 because everything is in service of the story with a logical progression. It's a large focus of the game.
Meanwhile in Heroes, none of the levels have any connection. They go to the tropical level, then a metropolis, then a casino, jungle, castle, etc. You could put them in any order and the game would be the same. There's no plot relevance to anything, it's just trying to be like the old Sonic games where there was no explanation for why any of the locales exist. What plot is there is minor and irrelevant to the rest of the game. See: the Android Shadow subplot, Chocola and Froggy being kidnapped, and the Metal Sonic reveal that only comes into play for the final boss.