The CloudFront documentation states:
If you configure CloudFront to compress content, CloudFront removes the ETag response header from the files that it compresses. When the ETag header is present, CloudFront and your origin can use it to determine whether the version of a file in a CloudFront edge cache is identical to the version on the origin server. However, after compression the two versions are no longer identical. As a result, when a compressed file expires and CloudFront forwards another request to your origin, your origin always returns the file to CloudFront instead of an HTTP status code 304 (Not Modified).
Why doesn't CloudFront save the ETag of the file before compression and use it for origin requests, to allow the 304 code?