I wonder what would have happened if Sega came out with the Wii instead of Nintendo.

Dreamcast 2 launches in 2004. It's a little more powerful than the OG Xbox. Most people just see it as a way for Sega to finally catch up to the other Gen 6 consoles in power. But many gamers just accept that Sega releases on a slightly different schedule than all the others. DC2 is $300 at launch and has Shenmue 3, Panzer Dragoon Penta, DVD playback capability, Virtua Fighter 5, Sonic 04 (just as bad as Sonic 06), and a ton of Japanese devs that made OG Xbox games. DC2 winds up being the first console to prove that less power is more. Games get released for it faster than 360 and PS3. It's significantly cheaper than everything except the Wii. Nintendo and Xbox 360 sales suffer due to DC2 being a stronger brand. In fact the 7th gen becomes a Wii vs DC2 shootout with the 360 and PS3 competing to see who can make it to 70 million first. Wii and DC2 both sell 85 million units easily but DC2 just has better 3rd party support later in the generation, which causes it to push 100 million units by late 2011. Then the DC3 launches and sits comfortably somewhere between Wii U and PS4 in terms of power.

Gamers overall stop caring about graphics. Arcade fun never dies. Sega never dies. Physical disks continue to get printed until the year 3000. My girlfriend finally agrees to that threesome with her best friend. DC3 is fully backwards compatible with all Sega consoles.

Sega identifies the lack of DVD support as a key factor for the Dreamcast’s lack of success. They partner with Toshiba and makes an HD-DVD based console. Because of Segas investment, the format is ready for the launch of their console in fall 2005. We get a console war that is also a film format war.

Dreamcast died before the 6th Generation fully started. Most multiplats were PS1 and N64 games. That makes it tough to know how Dreamcast would've ended up surviving longer.
But as clarification from the OP said, Dreamcast in this situation would finish around GameCube and Xbox still orders of magnitude below PS2.
The 7th Gen would potentially launch in late 2004, but no later than late 2005 right around the time Xbox 360 launches.
It would be relatively similar to Xbox 360 with no built in Wi-Fi or HDMI at launch. DVD support, a controller like Xbox, more powerful than OG Xbox and Wii but likely below Xbox 360.
I don't see it getting close to the other 3. I just don't.