> Building a streaming service is pretty expensive..
It's not. At least not for companies of that size. There is PeerTube for that: https://joinpeertube.org/. It can even decrease the load to your servers by spreading the trafic over peers.
Which problems are you expecting if you already have the content, the servers and the software? It's a famous company; people would definitely watch their movies for a small payment or with ads.