Well, that can be a double edged sword- seems just as likely that 3rd parties would complain about Nintendo's first party output taking away sales from whatever they brought to launch. Also, Nintendo had Zelda at its last launch and 3rd parties did not bring anything real significant to the platform until DQ:Swords in the summer of 2007, which frankly was pretty casual anyways.
I would also argue that at least in Nintendo's mind MH 3G HD was the game they felt would show 3rd parties that there was an audience for core games at launch. Outside of Zelda, not sure any Nintendo 1st party core gamer focused output would sell better.
While I'm sure some people would complain, I think a previous point we discussed kind of covered the answer to what tends to happen though.
The Wii had Wii Sports, Wii Fit, Mario, and Mario Kart, and Nintendo's support third party support ended up being minigame compilations, exercise games, a few platformers, and some knock off kart racing games.
There were also a ton of lightgun games after the success of Umbrella Chronicles.
As much as publishers may complain about having competing software, the way they treat platforms tends to suggest they like it.
Now, of course, most of those were low budget, but let's take Zelda as an example. Nintendo didn't get a lot of support in terms of larger core games from third parties, but I do feel it's worth noting that Beyond Good & Evil showed up on the GameCube, Okami showed up on the Wii, and Darksiders 2 showed up on the Wii U. None of these were exclusive, but they did at least get ports of these games, and I suspect Zelda had a fair amount to do with it. At least for Darksiders 2, Danny Bilson even said as much.
Did developers show up with games that were like RE4 after it showed up on the Wii U? No, but I do feel it's key that it was a budget re-release and a late port, whereas Zelda, Umbrella Chronicles, and the previously mentioned casual titles were all exclusives, suggesting that their audience was established on the Wii instead of also established on other platforms.
But yes, in terms of making larger sellers, I think they would have had to invest in new IP (or make a big push on a smaller IP) to attempt to do this.
I do feel Monster Hunter is an interesting example, but that what hurt that one was that it was an HD port of an existing game that sells better on PSP and 3DS. If you're making a hunting action game, why wouldn't you go with the PSP, 3DS, or Vita (given that many of the people making hunting action games may have thought mainline Monster Hunter was coming to the platform when they started) instead?
Monster Hunter also wasn't really announced early enough for publishers to see that and go "Oh, there may be a market for Hunting Action games here." Announcing what types of games you want on your platform early and often can be an effective tool in trying to influence developers, but Nintendo is fairly secretive.