size_t is only guaranteed to be large enough to store the size of the largest object. This is not the same as being able to index all of memory.
You could imagine a platform with restricted continuous allocation size where the maximum object size is smaller than the size of the address space.
Furthermore, size_t bears no relationship with int; it could be wider/equal/narrower. If size_t is narrower than int, then doing any arithmetic on size_t variables will result in automatic promotion to signed int, which can lead to dangerous signed overflow. C/C++ are full of footguns.
