Aside from the PS2, Nintendo owns the top 2 to 4 best selling consoles of all time. All three of them are cartridge based, included their most recent console.
They may have been outsold in the fifth generation of consoles, but first party software gave them longevity that their competitors wish they could replicate. Where is Master Chief and who, Crash Bandicoot, now?
The switch and DS aren't cartridge-based in the same sense at all that the SNES and N64 were though. The progression was generally:
ROM - VERY fast but small
Optical disks - slower but much larger
Flash carts - best of both worlds by the time we started using flash for game consoles
Nintendo f'd up by staying on ROM carts for the N64 because it limited your storage space so much. And the benefit - faster load times - was probably lost on many people. (Notice how no N64 game has loading screens of any notable length). OOT just uses brief fades to black.
If you can consider a Mascot something non-exclusive to the brand, introduced fourteen years after the release of the Xbox, and brought on through an acquisition, then sure.
They may have been outsold in the fifth generation of consoles, but first party software gave them longevity that their competitors wish they could replicate. Where is Master Chief and who, Crash Bandicoot, now?