Maybe they need it? A router isn't a home server. But even if, why do you keep your power efficient router running 24/7? You could turn it off when you're not home to save even more energy.
> a full-fledged PC (probably consuming like x100 the power
Maybe do some research before claims like these. He states this pc idles at 48W. Please show me a router capable of handling 25gbit/s that consumes 0,5W at idle.
> how would you build a "something" that monitors the network for packets sent to powered-off machines, then somehow caches the request, powers the destination machine On, and finally lets the request continue to its target?
That's what "wake on LAN" is for.