It isn't actually that flat in the spec, though modern machines' address spaces are. So in a sense it is merely an accident of a specific implementation that you can smash stacks.
Yes, you are right in that programs are not supposed to point outside of allocated blocks into other regions, that's UB. As in, pointer arithmetic that computes pointers outside of (but not even accessing!) an allocated block is UB. Annoying, pointers can legally be put into integers, looked at (e.g. printed out as a hex value), and then reinterpreted back into pointers, so it more-or-less dictates flat addressing. E.g. it's basically not possible to make an implementation that would run most programs where pointers are unforgeable, relocatable things, because of this. All of this spec is post-hoc, so it's a nasty retcon job that papers over the old folk understanding of one flat address space that's more or less still there in every implementation.
Casting integers to pointers is implementation-defined as far as I know.
Even if weren't, I'm not convinced that you have to interpret C's address space as flat just because it is finite or because pointers are representable as integers. In any case, machine's address spaces are flat (the physical memory mapped into them not so much), and working with real machines is what I'm interested in.
