TL;DR: Mario Kart or New IP are both possible, but I'd put them way down the list.
Prior assumptions:
Nintendo will develop the key launch title internally.
Nintendo will want a title that plays well in the West and in Japan
Next hardware is basically a Switch, doesn't need a Wii Sports style title.
Nintendo originally planned on launching this game in the holiday, before delays pushed to next year.
Studios that just aren't candidates at all:
NDCube, NST, NERD, 1-Up studios: all support studios, not really candidates.
EPD 1, 2, 6, 7, 11: Works primarily with external developers.
Studios that aren't really ready for new games:
Monolithsoft: Usually, 5 years between major games. It's too soon
EPD 3: The Legend of Zelda team. Tapped out.
EPD 10: 2D Mario, Pikmin. 2 games with lengthy development processes published last year. They're tapped out.
Unlikely for specific reasons:
Retro: MP4 is their comeback project, and the logistics of developing a launch title in Texas are very un-Nintendo.
NLG: Luigi's Mansion 4 is a dark horse title, since 3 did very well, and the original game was a GameCube launch title. But unlikely Nintendo planned 2 Luigi's Mansion games this year, even if Nintendo were willing to trust a recently purchased Western studio with the gig.
Remaining candidates in depth:
EPD 4: Smaller titles, made Switch Sports and 1-2 Switch.
These folks could make a game next year, they're pretty prolific. They own the legacy of the Wii Sports games, they made a Switch launch title. If there is a second launch title, the "casual" title, it's this team. But I don't think that's what OP was asking about
EPD 5: Nintendoland, Animal Crossing, Splatoon.
Honestly, this team should probably go in the "tapped out" list but it's just barely conceivable they could have something not-Splatoon this year. I don't think Animal Crossing is the right title to launch with, and Nintendo seems to like to let new IPs "bake", but it's not impossible this team delivers something.
EPD 8: Mario team, no major development since Odyssey, well over-due for a new title.
There is a reason everyone assumes 3D Mario. This is the team who have clearly been working on something for a while, and 3D Mario has been the least active of Nintendo's major franchises. Even the folks who don't think 3D Mario is the launch title assume it will come out in the launch year.
EPD 9: Nintendogs, ARMS, Mario Kart.
This team has been responsible for both the handheld and the TV versions of Mario Kart, before the Switch unified the hardware. If you slot in Mario Kart Tour as the "handheld MK we would have gotten" then they are just about due for a new game. If there is a Big EPD title in the first year that isn't 3D Mario, it's this team.