PeerTube
https://github.com/Chocobozzz/PeerTube
Will handle ridiculous amounts of traffic on a small server because popular videos are peered with other viewers watching the same video.
You can also federate with other PeerTube sites for more content, or just run your own instance with just your content.
It's free and open source but it's not simple to install. Once installed it's very easy to use and run.
I can install PeerTube for anyone who wants to run it for $75
You will need a bare metal server from Kimsufi, OVH, SoYouStart or Online.net or an instance from Vultr or Digital Ocean with the minimum following specs:
Ubuntu 18.04 LTS Bionic Beaver
4 Cores recommended
8GB RAM
100GB HDD minimum up to any maximum, more videos = more disk space
Root access
see a demo instance here:
https://peervideos.com
Video here:
Videos can be added easily.
You can upload videos directly, import from a URL or even import from a torrent file.
You can run unlimited instances and share videos between them seamlessly.
You have automated moderation tools, you can run an open instance or a closed instance.
The possibilities are unlimited with PeerTube.