There's a reason for why the Wii has a more diverse library of very popular games. Nintendo is the most diverse publisher in terms of genres by quite a large bit.
If you look at Nintendo's games 1.5 million plus sellers (I picked 1.5 million rather than 1 million because it removes the issue of what to do with remakes)
5 2D platformers
4 sports games
3 mini games
2 fitness games
2 3D platformers
2 action adventure games
1 third-person shooter
1 first person shooter
1 RPG (2 if you choose to count Super Paper Mario, in which case, move one from 2D platformers to here)
1 Simulation game
1 fighter
1 racer
1 music game
(I may be missing a game or two)
There's essentially a game in every genre. The only two I'd say are lacking from the list is "sandbox" and "strategy". For strategy, the problem isn't the lack of the games, it's that they're not selling. You have both Fire Emblem and Battallion Wars, and if things had gone as they intended, you'd have had a Pikmin game too.
The only genre Nintendo really makes an abundance of games in is 2D platformers. Apart from that, they've made at least one well-selling game in every single genre, with the exception of sandbox.
