This is coming with wayland and xdg-app. I say this not to try to refute your point but to give you something to Google for if you're curious about how things will probably work in the future.
Android it just that, and what they do there is run each app as its own user.
Though, Android also uses SELinux. I am not sure I would consider SELinux part of standard Unix permissions.
Imagine mobile OSs with just the Unix permissions system, the malware spread on those would be so humongous, it'd almost be funny again (arguably this was a long-time problem anyway privacy-wise, with software requiring privileges that couldn't be faked (e.g. giving the application a fake address book instead of your own), but at least apps couldn't easily nuke/hijack all your personal files.)