Because their focus was primarily on family-friendly games - or at least, up until recently, where they've begun to take a grittier turn. A change of hearts, of sorts. They're not so focused on the colourful aesthetic they used to have but I'd say it's still there to some extent, especially compared to their competitors.
Xbox and PlayStation, meanwhile, have always focused much more on darker games like FPSes. Or so it seems. Especially the former, I've heard they tried to introduce a more family-friendly mascot but that idea failed miserably. So they stuck to Master Chief. The latter at least had Spyro the Dragon and Crash Bandicoot.
Nintendo, meanwhile, what are their darkest mascots? Samus, perhaps. She's about it and even then she's more colourful then most of Xbox and PlayStation's mascots. Fire Emblem? Well, those are some dark stories, but it's still only fantasy-themed. And it wasn't until recently that FE was considered a major IP.
I think it was with the rise of FE that Nintendo became less family friendly. And perhaps with the new darker direction they're taking Zelda in. As well as the various ports of games such as Dark Souls and Skyrim. But their focus is still primarily on Mario and Pokemon and the like, all their family-friendly series, so I think it's fair to say they're still family-friendly.