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For sites with smaller servers, or limited drive space, being able to resize the locally saved version of an image (the "proxied image") would save on their resources and would also let their visitors on slow connections have faster response times.
Also, people can abuse the proxy - by manipulating images so they become very, very large. Then possibly use those in co-ordinated attacks to slow down your server. (Also depends on whether the proxy takes an exact copy or processes it first to optimise the size)