I have a question about this simple network;
With this simple setup shouldn't PCA and PCB be able to ping all of the 192.168.1.x addresses without setting up any routing, because the router 'knows about both 10.1.1.0 and 192.168.1.0 networks?
No, not necessarily. The servers need routing information to the 10.1.1.0 network and the PCs need to have a route to the 192.168.1.0 network. That may be a default route in both cases, but without a route matching the network "on the other side", the ping will not work.
And you need it for both: servers and pcs, because for a working ping, it is necessary, the ping request pass the network in one direction and the ping answers are able to pass the network in the other direction. Without bidirectional connectivity, you will never have successful pings.
Just as i wrote: you need a route matching 192.168.1.0 network on your PCs towards Router0 (it doesn't matter, if it is a route for 192.168.1.0/24 or a default route or something else, which includes the server ip addresses) and a route matching your PC ip addresses on the servers towards Router0 (it doesn't matter, if it's a default route or not, as long as it matches both PC ip addresses). Without having routing information that matches the servers ip addresses, the PCs would drop packets to the servers instead of sending them, because they don't know a route to the destination ip addresses of the packets. That was exactly, what happened without the default route. To make the ping successful, all devices "on the way" (beginning with the PCs and including Router0) need routing information for the target addresses of the pings (the servers ip addresses), and also the "routes back to the source of the ping" are needed on all devices "on the way back from the servers to the PCs" (beginning with the servers anbd including Router0). If there would be more routers "on the way", they all need routing information for the source and destination of the pings, otherwise the ping will fail.
Adding something else.
The router can apply routing between networks connected in its interfaces directly,
Each interface of router is a broadcast domain.
Example, considering the hosts are connected and configured correctly with its default gateway: All PCs have connectivity
If you connect to router with another layer 3 device with another networks connected to it, then you must apply a routing protocol between the devices to reach the networks you don't have connected in the local router.