Fabian

NES: SMB. No MK game.

SNES: SMW. SMK released a year later.

N64: SM64. MK64 released 3 months later.

GCN: Luigi's Mansion. MK:DD!! Released two years later.

Wii: LoZ:TP. MK Wii released two years later.

Wii U: No Mario/LoZ game. MK8 release two years later.

Switch: LoZ: BotW. MK8D almost two months later.

Mario Kart might be a console mover but it's not a console launcher which it carries more importance because it helps establish user base. Usually a console launch day experience is a single player experience, not a party one. Nintendo knows this, that's why MK is used as a mover not a luncher.