Two answers.
First, it does save money. A meaningful percentage of videos on the internet are never watched in the first place, and an even larger percentage are watched soon after upload and never watched again. We're able to prune unwatched renditions, and if they happen to be requested years later, they're still playable. Transcoding on the fly lets us save both CPU and storage.
Second, it is ridiculously fast. Our median time-to-publish for a 5-20 minute video is 9 seconds. We had a customer (God bless them) complaining a few months ago that it took us something like 40 seconds to transcode a 40 minute video, which actually was slower than normal for us. If you do an async transcode up front, you're looking at 20 minutes, not <1 minute.
Blog post on this: https://www.mux.com/blog/how-to-transcode-video-100x-faster-...