I'm not very familiar with the channel, but from the little I've seen, I believe the educational nature (and thereby fair use defense) could be debatable. Even if some of his videos are clearly educational, it seems that some videos are just covers of popular songs. And even if he's not using published sheet music to play the songs, he may still be required to have mechanical licenses, and possibly also sync licenses.
Most published music has three licenses that could be relevant here: the mechanical license (covering the combination of notes, rhythms, and/or lyrics that make the song distinct and "recognizable"), the sync license (using the song along with images/video), and a master license (covering a specific recording of the song). From my limited experience (and confirmed here [1]), it appears that many of these videos probably require at least a mechanical license to be performed publicly on the channel.
That being said, I absolutely agree with the sentiment that YouTube's handling of these issues is extremely problematic. They really need to start treating content creators with more respect and assume innocence until proven otherwise. There also needs to be more transparency into the process (and claims) so creators aren't left in the dark, along with improved ways to respond to erroneous claims.
[1] https://www.legalzoom.com/articles/posting-cover-songs-on-yo...