If you removed the Wii's GC backwards compatibility, you'd be taking out it's processor and graphics chip/card. When you're playing a GC game on the Wii, the processor literally works at the same speed and efficiency as the Gamecube's did, rather than at full power, as it would with a Wii game.
This is why developers have stated before that the Wii is GC 2.0 or even 1.5. It's literally more of the same.
Wii hardware has not gone down in price for one reason: It still sells. It sells at the price margin it is for sale at now. Sales are just now beginning to slow, and so price might lower in some time, but it has nothing to do with the components of the hardware, and everything to do with demand.
Alternatively, the Wii could be re-released in a black color, like it will in August in Japan. That could raise demand for the Wii, and keep the price from needing to be lowered. Nintendo likes to use new colors or package new software to raise demand rather than price drops, and like to hold on to pricing as long as it can sell.
Edit: They could easily increase the onboard flash memory from 512 MB to something higher, but there's not much reason we'd want that. The larger the flash memory, the higher premium we'll have to play. You'd be better off expanding the memory on your own through the SD card slot, looking for a deal online, or something similar. It's characteristic of consoles that when the console's maker does something the user should be able to do on their own, a premium is charged, and functionality is lowered. For example, look at the 360's HDD and contrast it to the PS3. With the 360, you need an official 360 drive, a device that comes in only a few sizes, and each is very overpriced. With the PS3, you can connect your own drive, which is much less expensive, and can be used with a computer in conjunction, among other things.