That make me wonder how hard it would be to just strip the bad functions out of the library.
Well your std c library is generally just a collection of .o, .a, .lib files. So you could use gnu bin tools to remove symbols of your choosing. However good luck getting your system to build software because that would modify the stdlib for all things compiled on your system. You could also tell gcc or clang not to link to the std library and providr your own with just a few switches on invocation of the compiler
Other thought would be to put the dlls with unsafe functions in different location than the safer ones and throw up a warning when an application loads them.