I couldn't find any more recent articles, although there were a whole bunch in 2009 about how much money it was losing.
https://www.itproportal.com/2015/02/26/youtube-still-loss-le...
I think an obvious but interesting thing about video-based business models in general is how their storage costs per video are basically indefinitely constant, but their revenue per video declines dramatically. 20 years from now Youtube might have 100x more content to store on their servers but it probably won't be getting 100x the views. I think the internet hasn't been around quite long enough for these kinds of things to become a real problem just yet.
You're already seeing this with the increased number of paywalls around publication content. I expect we'll see more subscriptions and services just shutting down if people aren't willing to pay.
Why can't they start deleting old videos?
That YouTube is a free hoster for video content wasn't inevitable and isn't guaranteed going forward into the indefinite future.
* Dailymotion (France)
* Flickr (United States)
* Metacafe (United States)
* IGTV (United States)
* Photobucket (United Sates)
* Twitch (United States)
* Veoh (United States/Israel)
* Vevo (United States)
* Vimeo (United States)
Vimeo in particular has about one-quarter the "market share" as Youtube [1]
[1] https://www.datanyze.com/market-share/online-video/youtube-m...