I'm a bit naive, but I don't think that's necessarily a requirement.
It might be commonly held convention, and thus, an assumption, in Linux (and, broadly, UNIX) but I don't think it's true inside VAX or even Windows, so I don't think it's a requirement.
Unless I've missed something (which is totally possible, this is not an area of OS design I've spent much time).
But also UID, groups, controlling TTY, process group, capabilities, pipes, shared memory, etc. and the file descriptors while maybe not inherently needed are how a lot of Unix plumbing works.
It might be commonly held convention, and thus, an assumption, in Linux (and, broadly, UNIX) but I don't think it's true inside VAX or even Windows, so I don't think it's a requirement.
Unless I've missed something (which is totally possible, this is not an area of OS design I've spent much time).