Why is it so difficult to make C less prone to buffer overflows?

Question

I'm doing a course in college, where one of the labs is to perform buffer overflow exploits on code they give us. This ranges from simple exploits like changing the return address for a function on a stack to return to a different function, all the way up to code that changes a programs register/memory state but then returns to the function that you called, meaning that the function you called is completely oblivious to the exploit.

I did some research into this, and these kinds of exploits are used pretty much everywhere even now, in things like running homebrew on the Wii, and the untethered jailbreak for iOS 4.3.1

My question is why is this problem so difficult to fix? It's obvious this is one major exploit used to hack hundreds of things, but seems like it would be pretty easy to fix by simply truncating any input past the allowed length, and simply sanitizing all input that you take.

EDIT: Another perspective that I'd like answers to consider - why do the creators of C not fix these issues by reimplementing the libraries?