Since large objects consume substantial resources, web proxy caching incurs a fundamental trade-off between performance (i.e., hit-ratio and latency) and overhead (i.e., resource usage), in terms of caching and relaying large objects to users. This paper investigates how and to what extent the current dedicated-server based web proxy caching scheme is affected by large file transfers in a high bandwidth campus network environment. We use a series of trace-based performance analyses and profiling of various resource components in our experimental squid proxy cache server. Large file transfers often overwhelm our cache server. This causes a bottleneck in a web network, by saturating the network bandwidth of the cache server. Due to the requests for large objects, response times required for delivery of concurrently requested small objects increase, by a factor as high as a few million, in the worst cases. We argue that this cache bandwidth bottleneck problem is due to the fundamental limitations of the current centralized web proxy caching model that scales poorly when there are a limited amount of dedicated resources. This is a serious threat to the viability of the current web proxy caching model, particularly in a high bandwidth access network, since it leads to sporadic disconnections of the downstream access network from the global web network. We propose a peer-to-peer cooperative web caching scheme to address the cache bandwidth bottleneck problem. We show that it performs the task of caching and delivery of large objects in an efficient and cost-effective manner, without generating significant overheads for participating peers.