Earlier quoted context omitted.
Routers are on the front line of computer security. They need to be very resistant to attack. Patch and release won't work; many routers never get patched, and those that do implicitly have a backdoor in the update system. This is a job for a limited protected-mode OS that Just Works. L4, QNX, something like that.
Or you could go the other way and use SELinux or similar, together with lots of hardening.
For web attacks, the web UI has to be quite privileged unless you explicitly privilege-separate it, Sandstorm-style. That seems like a big project for a router.
For kernel attacks, SELinux just increases the attack surface. Throw a good seccomp filter at things, deny access to proc and sysfs to things that don't need them, and use hardening options.
The trouble with anything other than Linux or maybe FreeBSD is driver support. And, for a router, even if an attacker merely compromises the network stack instead of compromising the whole system, the attacker still mostly wins.
What would be interesting is a good verified boot or immutable storage model. For example, have the router boot into a mode in which it can't write to persistent storage unless a physical button is used at boot time. eMMC can do this, but I have no idea whether the NOR and NAND chips in most routers can.