The benefit of the YT claim system is that 1) it usually gives a good enough remedy to copyright holders such that they won't feel the need to file DMCA takedowns or lawsuits against creators 2) it isn't subject to the DMCA's repeat infringement requirement (which manifests itself on YT and most other platforms as a 3-strikes-your-out policy) 3) it offers far more granular remedies (a claim won't always result in the video being taken down for instance) and 4) it's optional! If a claimee is willing to defend their content against a DMCA takedown or in court if need be, then they can always dispute+appeal
On the other hand, one of the big disadvantages of the claim system is that it makes navigating YT copyright confusing as hell to those unfamiliar with it. The misinformation that's so prevalent on the claim system just makes everything so much worse. Not entirely sure how YT could improve that TBH.