[ycmbntrthrwaway]

What you describe is called "namespaces". Plan 9 and Linux have them already.

[yiyus]

In Plan 9, special measures were taken to get dot dot right, not so much because of private namespaces but because of bind.

http://doc.cat-v.org/plan_9/4th_edition/papers/lexnames

[cyphar]

For those uninitiated to Plan9, binds are basically the replacement for symlinks (they're kind of like a mix of mount namespaces and bind mounts but more fundamentally baked into Plan9).