Currently net.TCPConn has dedicated support for this, but only for LimitedReader. Having dedicated support also for SectionReader would allow using the same FD concurrently to send the same file to multiple TCP connections, as well as supporting other use-cases (e.g. range requests).
This is obviously currently possible but without zero-copy support, resulting in the fallback genericReadFrom being used (that, in addition to requiring more syscalls, also requires more allocations):
I have a PoC for this on deea4f6