Like the internet, most of our programs are not peer-to-peer. A peer to peer program communicates with other instances of itself without storing its data on a central server. Such programs are very useful when workload needs to be distributed amongst various systems. Such systems are much more resilient than a server based system. Disabling the central server does nothing to prevent the peers from communicating and carrying on their work. Disabling the nodes in the peer to peer network simply removes that particular peer from the network. The other peers can continue to function and recover easily from the loss of that peer.
Such systems can be used to effectively distribute workloads from one system to another and complete data processing tasks much faster. For example: in a typical office, most workstations lie idle after work hours. These idle hours can be exploited to reduce workloads on other core systems.
A peer to peer based system needs a high capacity network to ensure that data moves efficiently from one node to another. A distribution and control framework can ensure that tasks that are distributed to various systems are tracked and completed. Such a framework would need built in security mechanisms to ensure that problems [viruses, malware, and spyware] on one node are not quickly replicated to another node. The framework also needs to ensure that the entire system can recover from the loss of a single processor or data. Furthermore, the framework also needs to implement authentication and authorization to ensure proper administration.
A load balancer would be needed to ensure that the individual nodes are not overloaded. Such a system would be well suited for tasks that require large processor resources. An array of such nodes could possibly be rapidly structured to perform various tasks based on the requirements of any given day.
Such frameworks would be really useful for anyone crunching large amounts of data, for example financial companies. Why buy a mainframe when you can use the office computers for the job.