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Content ID exists so YouTube can ease big partners.It's probably more to ease their own burden. YouTube likely receives a huge number of takedown requests daily, but with Content ID a lot more can be automated. Also, without Content ID, there would probably be a lot more companies just doing poorly-scripted takedown requests, which would make the experience of everyone on YouTube a lot worse. See: https://www.eff.org/deeplinks/2015/02/absurd-automated-notic...
> I am not sure about the three strikes being a part of DMCA. Are you sure?
The DMCA includes a clause about the termination of "repeat infringers"; I assume that YouTube's strike system is their easy-to-understand-and-apply way of addressing that. From the DMCA:
"The limitations on liability established by this section shall apply to a service provider only if the service provider has adopted and reasonably implemented, and informs subscribers and account holders of the service provider’s system or network of, a policy that provides for the termination in appropriate circumstances of subscribers and account holders of the service provider’s system or network who are repeat infringers"
(source: https://www.law.cornell.edu/uscode/text/17/512)
As for your last point, that does sound broken. Perhaps the content owner of the song you used decided that they didn't want people using it on YouTube after all?