Another way to look at this, you note you have 4 or more distribution routers. Without any core, how would you interconnect them? You could do a full mesh, but that is one connection from each distribution router to every other. Besides the problem of physical wiring topology, especially if the distribution routers are not near each other, it also adds to the complexity of the logical topology. (For instance, more routes to pass around within the routing protocol.)
If instead we have a core, we can run one link from each distribution router to the core. This avoids the full mesh complexity as you add additional distribution routers. It also simplifies bandwidth measurement, instead of watching bandwidth on every link between all the distribution routers, we only need to watch the bandwidth to the core.
If you can see the advantages to having a core with multiple distribution routers, the other important questions might be should the core be L2 or L3 and whether it should be dual core.
Traditionally, switching was much faster than routing, and if the distribution is routing, routing in the core seems a bit redundant and might slow the network down. So, the older design philosophy was to use L2 in the core.
Modern L3 switches usually approach L2 in speed, negating that consideration. Second, having all your distribution routers peer on a L2 segment does raise some other issues, one being multicast. The latter has been addressed by Cicso with technology such as PIM snooping (not ICMP snooping), but routing within the core also addresses the problem. Today, routed cores are recommended.
On the issue of core redundancy, since the core is so critical, we don't want a single point of failure. Hence the common dual core approach. However, it can also be addressed by a router with very few, if any, single points of failure. Examples would be 4500 or 6500 series with duals sups and power supplies and multiple line card links, or by the 3570 and 3750-E series as a stack. Using this type of equipment, one physical core might be adequate.
Lastly, I often remind people that your logical topology doesn't always have to be your physical topology. A logical core is a good thing, but does it have to be on its own physical platform in all cases? Sometimes it's not really necessary. You could place your logically core on one or two of your distribution routers. You even have the choice of it being L2 or L3. I sometimes suggest the server distribution routers for the co-location. The reason for placing it there, those routers already usually pass all traffic except client-to-client, which is often light.
