The video covers this aspect. Yes, the current system is bad, but it replaces a scary letter demanding cease and desists plus high damage payments and a resolution between extremely expensive lawyers. It surely is not optimal, but I doubt your common YouTuber could afford to fight claims in court.
DMCA replaces the scary letters. YouTube only responsibility is to collect claims and counterclaims. Common YouTubers can just accept the claim and mute content. Youtuber wanting a fight or that know the other party would never risk their frivolous challenge to go to court with the threat of perjury hanging on their head have a right to counterclaim and put the ball in the other party field.
YouTube instead decide to act as jury and will allow claimant to counter the counterclaim, and here lies the crux of the issue.
YouTube isn't protecting poor youtubers anymore than what DMCA already allows; YouTube is instead actively removing youtuber right to challenge the claim, putting all the power in the claimant, far above what DMCA mandates or requires.
And that decision to act as jury and judge and final unappealable authority in the claim process lies squarely on YouTube shoulders.
I don't think the DMCA replaces the scary letters. The scary letters existed because they were more effective than the DMCA. Threatening to sue someone is always and always has been totally an option. The reason scary letters don't get sent right now is because it's easier to just have Youtube remove the video.
If that went away the next easiest option (scary letters) would happen again. DMCA or not.
That's a US-specific issue. Yet people all over the world are affected by ContentID (though at least in the EU AFAIK you can now get a third party to mediate this dispute).