Why isn't a pointer null after calling free? How unsafe is it to use (assign, compare) a pointer value after it's been freed?

When you call free, the memory pointed to by the passed pointer is freed, but the value of the pointer in the caller probably remains unchanged, because C's pass-by-value semantics mean that called functions never permanently change the values of their arguments. A pointer value which has been freed is, strictly speaking, invalid, and any use of it, even if it is not dereferenced (i.e. even if the use of it is a seemingly innocuous assignment or comparison), can theoretically lead to trouble. (We can probably assume that as a quality of implementation issue, most implementations will not go out of their way to generate exceptions for innocuous uses of invalid pointers, but the Standard is clear in saying that nothing is guaranteed, and there are system architectures for which such exceptions would be quite natural.)
When pointer variables (or fields within structures) are repeatedly allocated and freed within a program, it is often useful to set them to NULL immediately after freeing them, to explicitly record their state.