Any arrangement that isn't star topology, needs every computer in the network to have multiple NICs, and must be configured to act as a switch, aware of all the other routes of nearby PCs.
Switches, and even hubs, have lots of NICs, as it were, and are really good at acting as switches. The network stack of an office PC's OS might be less good, meaning yes you'd have less equipment invested but all the packets would probably take longer to get where they needed to be.
Ring topology avoids the hardware requirements but every packet has to be examined by every PC, and for each packet the PC will either grab it, thanking the mailman as it were, or shakes it head "Nope, not for me -- try down the road I guess."
The dilbert strip about making the PHB look through the carpet for the dropped token is of course silly -- except it works like that. If there's an open port, the packets can't traverse the network properly and everyone is now disconnected until either a terminator is attached to the "dead" spigot or the cable is firmly reattached to the NIC and the network has a chance to restart.
Which NIC broke the network? Why, the one that's loose and wiggly of course!
You! Check your cable! Do it right or we have two breaks in our pipe!
This is why we all use ethernet going to a switch in the star topology. Everything works pretty well that way.