The smartest technologists and developers of our generation go to work for companies like Google, Amazon, Microsoft, Facebook, and others, and what we see are these results. Why can't we do better for everyone?
This claim process takes place before the legal copyright claim process. The legal process would require YouTube to take the video down immediately, and it would be required to stay down for at least two weeks even if the claim is bogus. (Or YouTube could decide not to follow the process and be held liable in case of actual infringement.)
There is no presumed innocence. The DMCA is constantly being abused, and the only possible punishment for malicious claims is an expensive lawsuit. It wouldn't surprise me at all if half of all DMCA takedown requests would be considered fair use in court, but the vast majority never get there.
Just think about how much money people have saved from DIY projects on YouTube, for example or how skills have been learned.
But currently the problem is that in aggregate, it brings more money to rely on an overreaching algorithm (which is already built and paid-for) that favours big established labels as opposed to small-scale creators; the money they would spend on ensuring everyone gets paid fairly by building a better system wouldn't be recouped by the (relatively small) revenue they'd get from small-scale creators being able to participate.
When I mentioned financial incentives, I didn't really mean incentives in terms of making more money - as per the above I don't think there is enough money to justify improving the current system. What I meant is that there should be more enforcement; what the current system does is actually committing copyright infringement by misattributing the revenue to the wrong creators, and if this was punished appropriately it would provide a financial incentive to resolve this problem.