Dragon Quest and Monster Hunter are both series that shoot for the most popular game system in Japan.
With Dragon Quest, it jumped to the PlayStation and PS2 because those systems sold way more in Japan than Nintendo's own systems, but then when the market started shifting heavily to handhelds the series moved to the DS, the most popular handheld of all time. The next game is on the Wii because it is the current most popular home system in Japan, plus I think the Nintendo audience is more receptive to the style of Dragon Quest than other systems.
Monster Hunter started on the PS2, and Monster Hunter Tri actually began as a PS3 game. But that was back when everyone thought the PS3 would reign supreme, once the Wii became a continued success the game moved to it. As for the PSP versions, I think the main reason it came to the PSP is because the DS isn't quite powerful enough to handle that kind of game. Hence, now that the 3DS came out and can muster the power needed, Monster Hunter has moved to the 3DS... with possible coaxing using the slide pad attachment. That's the closest thing Nintendo's done to a "moneyhat," though they didn't pay CapCom anything, they just made them a peripheral. Similarly, Nintendo made the Classic Controller Pro for Monster Hunter Tri.
So Nintendo aren't paying to secure these series, they just have the current most popular systems in Japan, and in MH's case are willing to provide accessories.
Also, there are a couple of HD Monster Hunter games in existence, they just weren't released outside Japan. The PS3 has an HD version of Monster Hunter Portable 3rd (a sort of remake of MHTri), and the XBox 360 has Monster Hunter Frontier Online (a port of the PC game).