One of the main complaints about Nintendo from gamers is it's lack of blood and gore in it's games, this can be shown from the thousands of threads on forums all over the internet, and indeed many threads on this forum.
The main complaint from 3rd Party devs is that they can't go up against Nintendo as they are simply too over powering on their own console.
These two reasons were valid on the GC because of it's kiddy image, it's small user base and little third party support due to nintendo's tough rules.
(I'm getting to my point read on!)
The Wii however has a very fast growing user base many of which did not own a GC last gen, it doesn't really have a kiddy image (yet) due to it's broader appeal and marketing. Third parties are being courted this gen by Nintendo, who have "done everything possible" to get GTA4 onto the platform and are allowing M/18 rated games on the system.
Nintendo are not creating such games. This allows Third parties to have this entire range of games to themselves with no challenge from Nintendo.
The fact that these games are in demand from the Wii user base can easily be shown by how well Red Steel sold even though it generally had poor reviews and had a very small user base at the time of release, the fact that RE4 is doing so well even though it is a (4th!) port also shows a strong demand from the Wii user base.
The Wii user base wants FPS, TPS, RTS etc games nintendo will not give them that.
3rd Parties Will.
With the (soon to be) No. 1 (current gen) user base exclusive games using the Wii remote to great effect is a good possiblity, they are already seeing that quick ports will not be good enough to sell there games.
So in Conclusion
Nintendo has left open a large portion of gaming genres for the third parties to sell to, all they have to do is make good games. The demand, user base and most importantly money is there for them to take. I expect the larger devs to do this and let the small devs make the cheap-but-interesting mini games.
"..just keep on trying 'till you run out of cake"