Significantly, shifting the image calculations from the server to the client means the work is duplicated for every client. While it saves energy for the server, it increases the overall energy consumption required to deliver the content.
False. Energetic costs of distributing duplicate information is significantly more expensive than local computation. Eg: measuring joules spent for decompression vs transmission is orders of magnitude over the n duplication.
But surely the orders of magnitude thing factors in when you can have orders of magnitude more clients than servers? I think you'd need to run more specific numbers to lean either way on this.
You seem to not realize that moving the calculation client-side means to send a JavaScript implementation, which for all sensible implementations would be significantly larger than the pre-computed result.