nine playable characters (even though only three have devoted campaigns),
All characters (including Metal Sonic as a 10th) were supposed to get dedicated DLC campaigns. Team Attack Amigo was clearly them scraping together the best of what they had and salvaging it.
God, imagine how insane they would have gone trying to make modified stage layouts for every single character, in addition to the ones already in game for Sonic, Shadow, and Silver (and Wave Ocean for Tails, Blaze, and Omega), in addition to the Hard Stages, the Very Hard stages, and the planned Super Hard stages.
There were a lot of things just wrong about 2006, and it did a terrible job communicating what I think it was supposed to be. (A literal "back to his roots," a retelling of the series as a whole, no continuity, telling a princess story in a way similar to some of the original origins of Sonic, although I'll grant not THAT similar.) Even if it was a glitch-free game that controlled beautifully... stylistically, story-wise, just in general, it would still need a lot of reworking. Elise's interaction with Sonic would have to be altered, and possibly have her family be changed to animals to match Sonic. (I didn't have an issue with it, since I knew they were going for the fairytale thing, but the "Oh god this is so horrible she's kissing a dead animal" chatter is overwhelming.) The whole cast needs de-lanked, when they were lanked in the first place to better interact with the humans, who are 95% of the time boring and generic as all hell and could use stylization themselves. Soleanna is incredibly boring, especially in the New City (notice how there is a ton of roads... and no cars?) or the amazingly empty forest. The dialogue should be rerecorded, the animations reworked, the list goes on and on.
I've daydreamed about "fixing" Sonic 2006 for years now, past when it's become anything resembling a relevant option. The question is, how much 2006 do you leave left over, and how much would you throw out and just remake? Would you just port what you could to the Hedgehog Engine and rebuild it from there? Would you try to patch up the otherwise janky and broken engine that they haven't touched in literally half a decade, if the same staff is even still available? There are so many questions and issues, and at best it would be an "image fix" for the series, trying their best to clear up the blackest spot on the series, or at least grey it a bit. It probably wouldn't be worth the investment, even if it meant they could start selling Sonic 2006 again, or if they could even convince old buyers to pay for the patch as DLC or an on-disc remake.
And the simple truth of the matter is that Sonic Team was already content to move on, while early restrictions on 360 patching may have made their life difficult, there wasn't much stopping them from silently fixing bugs for the reprints, for the Games on Demand version, etc. But they were content to continue shipping the same broken game right until it was pulled from shelves for good.