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To answer the "why not" part of that question, copying from one of my previous comments:
There's an enormous amount of content uploaded to YouTube, as much as 30,000 hours of video uploaded per hour. That's around 1PB per hour assuming most videos are uploaded in 1080p.
I wasn't able to find an official source for what YouTube's total data storage is, but this estimate puts it at 10 EB or 10,000,000,000 GB of video.
On Amazon AWS that would cost $3 Billion per month to store. The actual cost to Google is probably much lower because of economy of scale and because it is run by and optimized for them, but it is still a colossal figure. They offset the cost with ads, data collection, and premium subscription, but I would imagine running YouTube is still a net loss for Google.
Not that it makes much of a difference, but storing 10 EB on AWS S3 is more like 300 million USD a month. With some tiering options you can reduce that a bit further, but still it's a huge number. Following your link you seem to have used FSx Lustre for calculation, not S3.
That calculation may also take into account upload and download bandwidth. And I know there are like 100 different cloud products in the AWS console. I don’t know much about high scale performance tuning but I bet dozens of those AWS services would be involved in something like youtube.