You ever think about what they need to do to run it?
Originally the servers didn't need to handle that much
The way how YouTube gets money is by selling information of your interests to advertisers. The ads are from the uploader and the uploaders get the money. This is how Google, Facebook and other social media websites work. Google gets around a billion or so searches per hour, they get the money to run the servers because they sell your search history to advertisers. If you google "Rubber carrot" enough, you get ads about rubber carrots.