You do not have to register your copyright unless you intend to go to court. The DMCA should be a first notice of "I think you are offending, take this down so we can all avoid the trouble and cost of court". If you refuse to take things down than the claimant should get a lawyer, register the copyright, and go to court. However as first notice I want the DMCA take down to be simple and cheap for both parties if the guilty admits their mistake and fixes the problem. In generally nobody registers a copyright until just before they open a court case (you get triple damages for everything after the registration)
Where the DMCA went wrong in my opinion is it should have been upon notice you have one business day to notify whoever posted the content, and they get one business day to respond. If they take down the offending content, then all is well (the amount you could gain from two days of something being up isn't worth your court costs) If there is no response at all, only then is content taken down automatically. If there is a response that the content doesn't infringe then content stays up, but the response must contain full legal contact information: the accuser is required to go to court to get the content taken down. Note that court mean the count of law in the country the accused lives in.
The above is how normal cases should work. There are some tricky things that need to work different. If the accused is in a country that doesn't recognize copyright, if the legal contact information is invalid, if the accuser is submitting many false claims, or the middle party doesn't do their part there are problems. I'll post my ideas, but there is room for better ones and a lot of details need to be worked out.
If accused party is in a country that doesn't recognize international copyright (China being the big example), then take downs need to happen immediately - we cannot trust your courts to protect our people so you in turn are assumed wrong, take it up with your government. (I can't think of anything better here - I'm open to better ideas)
If the legal contact information given in the response is invalid, then the entire account should be terminated and all content deleted.
Many false claims needs to be legally defined. I'm going with the copyright owner and (not or!) their authorized agents send more than 100 take downs that after 1 year are still up and no court case has been filed.
If the middle party (youtube) doesn't react to court orders to take things down, or to the poster asking to take infringing content down then they are in trouble. Otherwise they are only a middleman.