I've worked for a major streaming company and with several other major streaming companies (including Twitch); I'd like to think I have a pretty good understanding of streaming costs.
> Youtube (very profitable)
The "very" part is probably not true, and that's with Google's massive advertising empire behind it. There's a good reason why Google is going so hard at anti-adblocker initiatives.
You can't run a profitable video streaming service with "just throw the video on a CDN" as the strategy, you have to be the CDN because at the scale you're operating at, you'll be murdered by external CDN costs.
But you're also correct that Twitch's content makes it incredibly hard to serve cheaply. Same reason why Mixer (competitor by Microsoft) folded so quickly and Facebook Gaming and Youtube Streaming have been neglected projects since launch.
There's only two viable video streaming business models right now: your content is essentially free (TikTok/Snap/Instagram), or your bandwidth is essentially free (HBO before the divorce with AT&T, maybe Comcast-Peacock+). Netflix sorta had near free content for a while before the studios cut them off.
I think Amazon was betting that AWS efficiencies could push Twitch into profitability, guess not.