We are serving static content over the internet, and have a business requirement that the data must be encrypted at rest. Currently it is stored in AWS S3, where it can be accessed by authorized clients over HTTP. We could proxy this through Cloudfront or Nginx to use TLS, but would only do so if it is necessary. The decryption key is retrieved by frontend client via a separate HTTPS request.
Do we gain anything by serving the static content over HTTPS, given that it is already encrypted? It brings added costs, infrastructure, and latency, and I cannot think of the benefit.