A thing that makes that complicated is that while you want that conceptually, you don't want that in reality. For instance, if the spawning process is in a container of some sort and it spawned a process that "shares nothing with the process that spawned it", the spawned process would no longer be in that container, because the state of "being in the container" is one of the things it shares with the parent process.

This is just an example of I don't even know how many things a modern-day process will share from its parent.

By "complicated" I do not even remotely mean "unsolvable". I just mean that if you really dig down into what it means to "share nothing" in a modern operating system, it's a lot richer than it was back when fork+exec was a practical solution. There's a lot of fuzzy things that could go either way when you say "shares nothing".

That’s how you get zombie processes and memory leaks.