I don't really look at Adventure 2 as a source of good ideas. When thinking about newer games (i.e. any and all games after Adventure 2), I kinda did the opposite: I looked at it to see what I didn't want in the next Sonic games. Back in the day I somewhat took the series' positive evolution as granted and thought "okay, the numerous bugs in Adventure 1 are because it's the very first full-scale 3D title and all these extraneous game styles are just marketing stunts to show as much of the Dreamcast's capabilities as possible, they won't be around in the next one", and later on "okay, with Adventure 2 they're trying to polish some of the first one's game styles, the story is worse than the first one but it's alright 'cause they didn't call the first one Sonic the Hedgehog 4, they belong to the 'Adventure series', so maybe it'll go back to the way it was sometime down the line"...
In other words, I was willing to put up with a certain dose of bull during Sonic's early 3D years, as long as the developers knew how to tell it from the good ideas and at least made a honest effort at keeping up the good work and coming up with progressively better and better games. But Heroes' premise and execution ground much of that hope into the dirt, and Shadow's premise alone was enough to crush the remains.
... And then came 06. They played with my feelings, they fucked around with my hope for the series. And I swore I wouldn't take no more bullshit.
And here I am. It's been ten years and one or two hardware generations since Adventure 2, and 3D action gaming has gotten as good as Bayonetta, Vanquish, Ninja Gaiden, et cetera. Remember when the first Adventure was said to "redefine 3D platforming"? How it was at the top of its game graphics-wise (I remember reading it was the single best-looking game until the DC version of SoulCalibur arrived a couple months later)?
This was a champion series, not once but twice. Now it's playing generic, low-budget, third-rate mascot-based platformer on underpowered Nintendo hardware. If I told all this to myself back in 2001, I'd have ended up in the hospital because of a serious contusion in the head for banging it against the wall multiple times.
tl;dr: Adventure 2 was okay by 2001 SEGA standards, everything after it were painful steps backwards doing nothing but repeating many of its mistakes and then adding their own, with precious few to no pros to speak of in a world that was being quickly populated with better, more focused 3D action games.
Adventure 2 was, back then, a AAA title. Now this series can't keep up with the big boys. And that's sad as fuck.
EDIT: Wow. I originally intended to write only what's in the first paragraph and one or two sentences of the second one. Guess I'm not over this yet.