With a 1Gig connection you can only serve ~45 concurrents streaming 1080p. If you wanted to support more than 45 concurrents, you would need
1. To distribute content to separate instances
2. A routing infrastructure to reliably route connections to that content.
And then, congrats, you have just built your own CDN - albeit in one datacenter. If you don't want your users on the other side of the country constantly complaining that your site is slow compared to Vimeo, you would have to build it on the other side as well.
If you believe your hodgepodge CDN is going to be much cheaper than Cloudfront (on the order of 1 Euro/month, where you could support it on ~1.5M views/month), then you should probably skip the whole video sharing nonsense, and get rich becoming a CDN provider :)
If you believe otherwise, please enlighten me on how you can build a HD video streaming service for 100 concurrents without a CDN. Like I mentioned, on a 1GbE connection, you can serve a theoretical max of 45 users on one node. Where do you go from there without something that looks like CDN?
But it's not. Your example is contrived, as Hetzner likely doesn't expect you to stream a 100 hours of 1080p HD content to 100 people simultaneously. Your users would have a laughably bad experience at scale. On a single box, it's unlikely you could max out your throughput - you could at most support 45 users on a single Hetzner node (1080p @ 22Mbps on a Gigabit connection in the best case).
If you are going to be serving content with any level of seriousness you need a CDN. 1TB of bandwidth on Cloudfront costs $87. Akamai charges $100-$150. Thats 100x than 1 euro/TB you initially priced out.