I'm going to say no, Super Mario has not surpassed Mario Kart in terms of capturing the minds of fans. And to prove this, I'm going to use the most scientific metric I can think of: memes.
Think about how many phrases and shorthands are taken from Super Mario. 1-Ups are still used to refer to extra lives in general, Ghost Houses is still used to refer to mazelike haunted locations in games, TV Tropes uses phrases like Lethal Laval Land and Shifting Sand Land to refer to Volcano and Desert levels, etc.
On the website Know Your Meme, individual memes are saved by a bunch of volunteers. It isn't scientific, but generally the more popular bits of culture are reflected in the numbers on this website. The "Mario Kart" entry has 11 sub-entries and over 530 images in its gallery. The Super Mario category? 73 sub-entries and over 4150 images. Super Mario Odyssey alone has a similar image count to Mario Kart, with 534 images in its gallery.
ANOTHER way to look at the question is in the games themselves. In Mario Kart, many of the tracks are based on themes and locations in the Super Mario series. In MK8, most of the roster had their debuts in platformers, tracks use series motiffs like airships and castles, and various sprites and visual elements from the Super Mario series litter the game. In contrast, how many Mario Kart elements appear in Super Mario Odyssey or Super Mario Bros Wonder?