If the image proxy keeps served images cached for a period of time, bandwidth probably won’t be an issue. But if the image proxy queries the storage bucket every time someone accesses the image, egress charges will quickly add up.
Caching is up to the browser, so it's a per-user thing:
The image proxy isn't a caching proxy. Proxied images are never saved to disk, and only small chunks of images are stored in memory at any one time. The proxy does work with client-side caching (it passes on appropriate cache-related headers, etc.), so you may cache images.
I suspect that is the underlying root cause of the imgur problems. If there is an image in a particular thread, the image proxy server may be asking for imgur to serve the same image multiple times over a short time if there is a conversation among several people. Replying to a post with an image may result in the same person causing the image proxy server to call the image three times, and this would not count the times the person reads a thread, but does not reply.
Imgur (in the past)
uses AWS, so they are paying the quoted prices for serving images to the forum image proxy. Serving only the image means imgur doesn't get any ad revenue from the forum.
Someone is going to have to pay to get images from wherever they are stored to forum users. It doesn't look like imgur is wanting to pay for this anymore.