A fan of Mario spin-offs Paper Mario and Mario Kart has created an exciting mockup of how the two might look when combined with each other. It's a real shame this isn't a Nintendo-made project, as the end result is surprisingly promising.
As far as Mario fans know, Mario Kart takes place in the same universe as the mainline Mario games like Super Mario Odyssey. The same can't be said for Paper Mario, which sometimes uses the paper-based nature of its world as a plot point. Paper Mario did actually cross over with the mainline Mario universe in Mario and Luigi: Paper Jam, where it was implied that Paper Mario takes place in a magic book contained in the "real" Mushroom Kingdom. Still, it's unlikely that anyone would hold it against Nintendo for adding Paper Mario to the Mario Kart roster.
YouTube user Banana Pictures created a robust proof-of-concept for a Paper Mario Kart game. The two-minute video includes a title screen, character-select menu with seven characters, and a lap around a racecourse. While the course is heavily based on N64 Royal Raceway from Mario Kart 8 Deluxe, the course looks very different rendered in a pop-up book style. Sadly, Mario is the only driver on the track. It would presumably be overkill to implement multiple on-course racers for a proof-of-concept, but it would be exciting to imagine how the various characters would interact with each other on the road.
Fans might be disappointed to see that the proof-of-concept's roster sticks to a simple cast of core Mario characters. Many Paper Mario enthusiasts point to the series' original characters as one of its best qualities, particularly those from earlier games like Paper Mario: The Thousand-Year Door. The simplest explanation is that Banana Pictures probably needed assets from the most recent Paper Mario games in order to create a high-definition proof-of-concept. As recent games feature few original characters, there simply wasn't much to choose from in compiling a roster.
Given the Paper Mario series' reputation for having humorous and exciting stories, it would be fun to imagine a Paper Mario Kart game specifically for its story mode. While recent games may not have the most exciting original characters, they do have exciting bosses that would fun to rematch in a go-karting context. Fighting Paper Mario: The Origami King's Legion of Stationary while in a kart, for example, would be especially fun.
While none of the current Mario Kart games feature Paper Mario in any way, it's possible this could change in an unexpected way. The Mario Kart attraction in Super Nintendo World, the new theme park attraction, is built on a game engine, meaning ride designers can modify it at any time. This means it would be possible to add Paper Mario at any time. It probably wouldn't fulfill fans' hopes for a real Paper Mario Kart game, but at this point, even a cameo in a theme-park ride would be a welcome first step.