It was out of self interest of course, but, Google did just finish a decade long, costing probably hundreds of millions of dollars in legal fees, battle with Oracle to fight for reasonable copyright interpretation for software developers.
This current situation on YT is the result of another multi-billion dollar legal fight with the music industry. I don't like how YT handles this either but I put most of the blame on the music industry for it.
Also remember Google Books, which was a huge (seriously, huge) project that spent years with full funding only to be killed by the publishing industry because they couldn't justify it under the notion of "fair use" we're stuck with.
you are getting to things confused here: fair use of copyrighted material, and being responsible and responsive for a quasi judical algorithmic process and its mistakes.
(remember its beethovens moonlight sonata, one of the most famous classical pieces period. i dont think you even could copyright a part of it, at least not just the sequence of notes)
This current situation on YT is the result of another multi-billion dollar legal fight with the music industry. I don't like how YT handles this either but I put most of the blame on the music industry for it.