Why no switch on pointers?

For instance:

#include <stdio.h>

void why_cant_we_switch_him(void *ptr)
{
    switch (ptr) {
        case NULL:
            printf("NULL!\n");
            break;
        default:
            printf("%p!\n", ptr);
            break;
    }
}

int main(void)
{
    void *foo = "toast";
    why_cant_we_switch_him(foo);
    return 0;
}

gcc test.c -o test
test.c: In function 'why_cant_we_switch_him':
test.c:5: error: switch quantity not an integer
test.c:6: error: pointers are not permitted as case values

Just curious. Is this a technical limitation?

EDIT

People seem to think there is only one constant pointer expression. Is that is really true, though? For instance, here is a common paradigm in Objective-C (it is really only C aside from NSString, id and nil, which are merely a pointers, so it is still relevant — I just wanted to point out that there is, in fact, a common use for it, despite this being only a technical question):

#include <stdio.h>
#include <Foundation/Foundation.h>

static NSString * const kMyConstantObject = @"Foo";

void why_cant_we_switch_him(id ptr)
{
    switch (ptr) {
        case kMyConstantObject: // (Note that we are comparing pointers, not string values.)
            printf("We found him!\n");
            break;
        case nil:
            printf("He appears to be nil (or NULL, whichever you prefer).\n");
            break;
        default:
            printf("%p!\n", ptr);
            break;
    }
}

int main(void)
{
    NSString *foo = @"toast";
    why_cant_we_switch_him(foo);
    foo = kMyConstantObject;
    why_cant_we_switch_him(foo);

    return 0;
}

gcc test.c -o test -framework Foundation
test.c: In function 'why_cant_we_switch_him':
test.c:5: error: switch quantity not an integer
test.c:6: error: pointers are not permitted as case values

It appears that the reason is that switch only allows integral values (as the compiler warning said). So I suppose a better question would be to ask why this is the case? (though it is probably too late now.)

Switch statements operate on integral values only. That's why the error message is "switch quantity not an integer." I don't think it's a technical limitation so much as it's outside the language syntax.