Nintendo is hosting a party that is going to be lame to begin with. That is the problem. That's why it is mostly their own fault. They host a party that caters specifically to themselves but is of little interest to everyone else.
I really don't think that the lack of third party support has nearly as much to do with the capabilities of the Wii as you do. I think a large part of it actually stems more from trend of decreasing support on the N64 and the Gamecube. Whether or not that is Nintendo's fault or not can be left for a different discussion. By the time the Wii came around third parties were already hesitant to support the Nintendo consoles. So when the Wii did release pretty much all that was available from third parties was rushed ports (Far Cry) and rushed games that did not live up to expectations (Red Steel). None of which left a very good impression for these companies.
Once the Wii's success became clear all of the third parties were caught off guard so had to rush to release more games that were again either rushed ports (Dead Rising), rehashes of games they already released (Rabbids 2 and Rabbids TV Party), or that didn't have enough development time. Which again didn't leave a good impression with customers.
So after a few years into the Wii's life some third parties finally got their act together and started releasing quality titles (Red Steel 2, Dead Space Extraction, Rabbids Go Home). By this time nobody is willing to buy there games anymore because there are afraid they will be crap. You have to make a market for you product by creating interest and earning your customers trust. Third parties didn't do that and Nintendo shouldn't have had to do it for them.
To say that it is all the fault of the Wii's capabilities or Nintendo's fault in general that there is poor third party support is ridiculous. Also, all of the complaints that you make about the Wii could be said about the DS, but it has some of the best third party support ever.
I could also make plenty of comments about your complaint about the Wii controller harming third party support. If I can use the Wii remote to control pretty much any game on the PC (Borderlands, Lara Croft: Guardian of Light, Dead Space, Runes of Magic, etc.) without any troubles then there is no good reason that third parties couldn't have made any PS3 or 360 game control fine on the Wii, also.
Regardless I agree that there is no hope for third party games on the Wii, but that still doesn't mean that Nintendo's core games can't be successful.