This is vaguely the idea behind Joanna Rutkowska and co.'s Qubes: there are lots of Linux kernels in different Xen domains, one for each class of userspace apps (banking, gaming, etc.) and one for each low-level service (networking, graphics, etc.). For instance, if the Linux kernel is vulnerable to a local privilege escalation, and the DHCP client is vulnerable to arbitrary code execution, on a traditional system, anyone on the other side of your Ethernet cable can root your machine. Under Qubes, all they can do is root the Xen domain that's providing networking -- but that's not significantly more power than they had than by being on the other end of your network cable, since that domain does nothing other than networking.
I'm not convinced that Linux is unkillable, though. This thread is about OS X, I'm typing this on an OS X machine, etc. I suspect that if you do a good job of working with people's hardware (Apple has an advantage, of course), you can run Chrome, and you can run anything that's portable between OS X and Linux, you can get pretty far.
https://qubes-os.org/
I'm not convinced that Linux is unkillable, though. This thread is about OS X, I'm typing this on an OS X machine, etc. I suspect that if you do a good job of working with people's hardware (Apple has an advantage, of course), you can run Chrome, and you can run anything that's portable between OS X and Linux, you can get pretty far.