What is the rationale for limitations on pointer arithmetic or comparison?

Question

In C/C++, addition or subtraction on pointer is defined only if the resulting pointer lies within the original pointed complete object. Moreover, comparison of two pointers

Answer 1

I would like to answer this by inverting the question. Instead of asking why pointer addition and most of the arithmetic operations are not allowed, why do pointers allow only adding or subtracting an integer, post and pre increment and decrement and comparison (or subtraction) of pointers pointing to the same array? It is to do with the logical consequence of the arithmetic operation. Adding/subtracting an integer n to a pointer p gives me the address of nth element from the currently pointed element either in the forward or reverse direction. Similarly, subtracting p1 and p2 pointing to the same array gives me the count of elements between the two pointers. The fact (or design) that the pointer arithmetic operations are defined consistent with the type of variable it is pointing to is a real stroke of genius. Any operation other than the permitted ones defies programming or philosophically logical reasoning and therefore is not allowed.