Interestingly they could also just keep the best resolution version of rare videos, and have really powerful encoders if anyone suddenly asked for a lowres version. Then they can deliver as well as cache the lowres version in case someone else wants to look at it an hour later, but maybe drop it after a week of no access.

They don't even have to be all that powerful. GPU transcoding is fast as heck. You really just need to decide where the line is between the storage tradeoff and needing a bigger GPU farm to handle more frequent transcoding requests. I'm betting you could get away with having just one copy for 90-95% of Youtube's content. There is an ocean of video on Youtube that is accessed less than once a month or even once a year.

That, and I’m sure they employ “cold storage” using slower (and cheaper) spinning disks.