I'm going out on a limb by saying Mario Kart may very well be the very first "mascot kart racer". Of all the recognizable VG characters (Pacman, et al.), I don't recall any of them in any sort of spin-off racing game released prior to '92.
Doesn't mean I'm done researching - I'm actually still trying to find an example prior to MK (Savannah, you had me excited there for a second

) but came up with nothing. If anyone else knows of one, please share - I am curious. BTW: We're talking a spin-off kart racer utilizing existing characters from another series of games. No, Outrun doesn't count. And technically, neither would ModNation Racers.
Though, undeniably, if Mario Kart isn't the first it certainly is the one that popularized the genre. Half the reason the other cart racers tank is the lack of popularity of the characters. Mario and his stable are insanely popular and recognizable by almost everyone. Sackboy? Not so much. Even Sega's racing roster includes Sonic, a bunch of forgettable Sonic sidekicks (and Tails), and one-off characters that have faded into history (for the casual gamers that is - calm down, Alex Kidd fans.)
For the record, the only company besides Nintendo that can possibly pull-off the "mascot racer" would be Capcom. But they wisely choose to let them beat each other up tag team style instead.