> walk around outside, making a video of what they're doing, and post it, without having to worry that some copyrighted music is playing in the background for some portion of it.

You can, this is called "incidental use" and is an exception to copyright in the USA. If you're filming yourself going down the street and someone starts playing a song, and you're not going out of your easy to capture the copyrighted content, it is legal.

YouTube's copyright strike system is more strict than the law, probably to kowtow to the music companies serving the YouTube Music product in exchange for not having to defend against a lawsuit.

If we weren't subject to their monopoly on online video, someone could just start telling copyright trolls to pound sand when a frivolous complaint comes up.