Some people want 480p video.
Some people want 1080p video.
Some people want 4k video.
Even if the browser <video> tag did a great job at codec and resolution negotiation you still have to encode _at a minimum_ three copies of the video to hit the qualities. Multiply that each time you need a different codec for different devices.
Or, upload one video to Youtube.
It means they want the video to be encoded in multiple resolutions for different levels of connection. Another thing that's not necessarily trivial, especially at scale.
I've fought and lost this battle many many times, and have used mobile bandwidth as a reason too.
High resolution video hosting/streaming is free, so no one wants to pay to host it. I think there are major downsides to hosting on YouTube, but in my experience the vast majority of people do not care.