I don't know the burden is as big as you imagine. I used to run a torrent site that was 99% recorded shows through capture and we still had every single broadcast show uploaded within minutes -- and no uploaders were getting paid, they were just bored and doing it for the Internet points.

edit: also to add, we would get employees at the studios send us discs with the new shows before release, but I had agreements with at least one studio to not allow uploads until after broadcast if we received any of their media