There are/were plenty of one port routers on the market, especially if we mean one LAN port.** That's all that are needed, and the minimal number of ports doesn't make it any less of a router. It just means you'll probably connect the switch of your choice to the LAN side rather than use the built-in switch (since in the case of a one port router there is no built in switch).
**Technically, a router can get by with just one port which would be used for both WAN and LAN, but I don't know of any examples of that, given the context of this discussion.I still don't know why there would be possible address conflicts, though. Properly configured, a router never has the same subnet on its WAN and LAN sides.
Oh, wait, Jeff mentioned that some DSL modem/routers default to a certain IP range on their LAN side, and adding a second router might introduce the possibility of THAT device also wanting to use that same IP range. But in his example, the DSL modem/router auto configured itself to avoid the conflict. The possibility exists, I suppose, that not all DSL modem/routers are smart enough to auto configure themselves that way, and some standalone routers don't give the user the capability to configure the LAN subnet. Nearly all of my recent experience is with dd-wrt, though, so configuring the subnet is second nature and I sometimes forget that stock firmware may not offer that.
Correct. If you use a switch with a combo modem/router device, the router in the combo device is where you'll make all of your configurations. However, if you add a second router in series, then it makes sense to "DMZ the modem to the router", as you call it, and then make all of your configurations in the second router.
Yes, I know "DMZ" is the wrong term for what we're discussing, but Linksys bastardized it long ago so I'm just using it the way they do. Network engineers no doubt are cringing, as they should.