Although it is a good idea, this had no impact. I did attempt a static address outside of the pool (of course, wouldn't step on the pool). However, this had no impact. Using the wired interface, it is now running on a static, outside of DHCP, and next to other IP based printers (I group for my convenience).
I find it a bit odd that the device must have exchanged ARP data (MAC reference data on the wire) with the router while static with the router. My guess is that this is either a bug with the DHCP addressing component of the printer, or having to do with the "gateway" which has always been properly configured. If I don't return the printer, and decide to look into this further, I'll follow up here.
From a technical perspective, communications with the LAN should not require any router support beyond the addressing from the DHCP server (not always a router function - just typically done this way today). On the LAN with 20 or so devices, this should occur equally with all devices (that is the function of ARP packets, of course). So, to this end, I'm not sure if you are thinking that this device must send data to the router? For reference, the router is not a WiFi device, a series of several APs provide WiFi in my home. So communications with the WiFi doesn't assure communications with the router - a critical component of this discussion.
