Why does *p++ increment the pointer, not the value?

Because postfix ++ binds tighter than *, so *p++ parses as *(p++): it dereferences the old p, then advances the pointer.

// Parsed as: *(p++)
*p++
       // 1. Returns current p
       // 2. Increments p (for next time)
       // 3. Dereferences the OLD p value

What each variation does:

int arr[] = {10, 20, 30};
int *p = arr;

// Returns 10, p now points to arr[1]
*p++
        // Equivalent to: *(p++)

// Increments p first, returns 20
*++p
        // Equivalent to: *(++p)

// Increments the VALUE at p (10→11), returns 11
++*p
        // Equivalent to: ++(*p)

// Returns value at p (10), then increments it (→11)
(*p)++

Common idiom - copy string:

while (*dest++ = *src++)
    ;
// Copies char, advances both pointers, stops at '\0'