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What's the point of this nitpick?

Networks that configure everything statically are fairly rare, and do so intentionally. If they don't, they have a DHCP server somewhere already, and if they aren't consumer-level networks they sure as hell don't want some random "IoT gateway" box providing DHCP. So it's clear what "router" means in this context.

I have a separate dhcp server so if the router has issues machines can still attach to the network and talk to local services.

In my experience the majority (all the ones I've owned at least) of consumer grade routers have DHCP.

Most layer 3 switches provide DHCP, and since almost all consumer routers also provide DHCP, probably most routers do provide DHCP.