But this means data transiting your network instead of being directly fetched from AWS infrastructure, which for me mostly defeats the purpose of presigned S3 URLs.
If your server is on AWS, then the egress cost should be identical whether the transfer originates from S3 or EC2. But if your server is on premise and your host charges for egress (or has impactful bandwidth restrictions), I can understand where you're coming from, as you could end up paying twice.