Sonic is defined by his style of gameplay at the time, not a title. 

Fallout 3 is vastly different from Fallout 2. I'm saying that as long as the game is really good, they can give it the Sonic Adventure 3 title and with that, people get a game they wanted while Sega is satisfied with its quality.

Not relevant.

How is it not relevant?

Sonic fans: When you ask for an Adventure game, What are you asking for? 

Yeah, the second I read this quote from Iizuka I thought of that quote from the trailer.

"But now, as we move forward; to discover what made Sonic a gaming icon, we're going back."

Sonic Team has clearly forgotten that the Adventure era was one of those things that made Sonic great. They really need to look back at that era again. Many people loved having multiple different playable characters with different playstyles for each, they loved the Chao Garden, they loved the music from that era with Crush 40 and Hunnid P killing it, and they loved having more open levels to explore as opposed to the more linear approach on more recent 3D Sonic games. 

I won't deny that Adventure had some issues. Big the Cat was a mistake for sure, and some of the other playable characters/playstyles weren't very well recieved either. But I think that's one reason why so many people want Adventure 3. They hope that Sega will take the good from Adventure 1 and 2 and keep it, toss out the bad, and maybe add a few new features that are cool.