Not only that, but having Bean (a troublemaker), Bark (an introvert) and Ray (a friendly dork) sounds like a lot of fun, specially if they're all trying to act as the 'leader' and taking the whole team in a different direction, only to fail and going back to square one

Another thing is Big's absense. I get that him being part of the team is kind of a joke itself, but I guess another fun way to use him in the game is treating him how SA2 did: make him randomly appear throughout the levels as a easter egg and as a gag

It would also work just as well in the team dynamic. Emerl is not a Eggman robot per se, but his character could revolve around that idea and Omega's interactions would be intact. Rouge would have no reason to NOT mention Emerl's past because she simply DOESN'T KNOW what that is

What if, because of the Chaotix' absense, Bark, Bean and Ray are the 'team of outcasts' of Sonic Heroes, who just so happen to stumble their way into the main story? (Modern Ray was also made by Prime-101, but I could not find the sources for Bark and Bean).

What if the Chaotix were not reworked into new characters, so Espio was the only detective (like his Classic counterpart) investigating Sonic's mysterious kidnapping of Chocola?

What if Shadow was not brought back after SA2, so Emerl replaced him as the character with amnesia of Team Dark?