To explore yet another view point, a router connects your LAN to the internet. A Firewall has the domain over traffic control.

Now, in a small SOHO network, a router is needed to connect the network to the internet, and due to the size and nature of the network, a single firewall at the LAN WAN interface is needed - the router would do fine here....

However, ideally you are wanting to firewall protect every segment of the network that is critical. In a large network, multiple firewalls would be utilised, and some to protect only a single server..... another firewall to protect the workstations (on the same physical or logical network) and yet another firewall to protect the file server, as well as a WAN LAN interface firewall....... and each would be configured uniquely depending on the requirements of communication between each 'firewall protected' segment of the network.

Ideally....

Anyway, my point is when exploring the debate from this point of view, a router is needed to translate between the LAN and WAN only, whilst a firewall will do the protecting and traffic flow at various points throughout the network. From this point of view, the router and the firewall roles cannot be interchanged.