Sorry, I've gotta be harsh here.
SEGA is great at making people happy. That's what hiring Christian Whitehead and crew to make a brand new Genesis era Sonic game is. It's about making the right people happy, and those are the people whose desires push the franchise back into a positive light, not further down the drain. Look at these happy people:
The happy ones have been with the series before the dark ages brought on by the Dreamcast. The Sonic Adventure games aren't flawed classics like Half Life or Ocarina of Time. they aren't rough around the edges like Mega Man Legends or Crash Bandicoot. They are fundamentally broken games barely above the likes of Ultima IX or Daikatana. The games from this era float entirely on nostalgia, proven by the unanimously negative reception to more recent Sonic games that share the same problems.
Sonic Adventure 3 makes as much sense as Mega Man X7-2. The idea of what a Sonic game is in 3D has fundamentally changed. If they made another one it would, and frankly, should, look and play like the Sonic Utopia fan project. That's much closer to what Sonic is and what the majority of the player base wants to see from the franchise. Making the game good by modern standards would make it Sonic Adventure no longer. People wouldn't respond to levels created that way or stories told in that manner. Tasted have changed and that era is over.
Dark and edgy Sonic clones riding motorcycles and sneering with loaded firearms played against hard rock cringe-lyrics is over. Bat cleavage is over. Animals kissing human women is over. Convoluted plots and nonsensical character motivations are over. This comment solidifies that SEGA is not keen on revisiting the exact elements that tanked Sonic's reputation as a character, as a brand, and as a franchise, and nobody should blame them.
That said, Sonic Adventure 3 does exist. It's Sonic the Hedgehog on 360 and PS3. Pretending it isn't is like pretending Mega Man Star Force isn't, for all intents and purposes, Mega Man Battle Network 7. Every element is still here. Nothing changed. There wasn't even a significant amount of time between the games. Sonic 06 could have been called Adventure 3 and no one would have skipped a beat.
Sonic Adventure 4 exists, come to think of it. That one's called Sonic Boom on Wii U. Broken set pieces, loops that take your controls and still manage to fail, voice acting as horrible as the dialogue, animations as awful as the controls, game flow as choppy as the level design, it's all there. BigRedButton even described their process as "getting back to the Sonic Adventure feel", so I can only imagine making it garbage was an intentional design choice.
The gameplay and style you remember from Sonic Adventure does not need to come back, but Sega isn't just ignoring people either. Chaos and Shadow are back for Sonic Forces and a playable Shadow segment was literally just announced. Levels based on the games you enjoyed were present in Generations. They aren't pretending you don't exist or that your favorite games aren't worth anything. They're just focused on making good products again.