Just how profitable does your business have to be before you can start hiring people? Apparently not even Google or Facebook or Apple have enough money to hire a bunch of minimum-wage help-desk employees to police content on their own sites.
Of course, we know it's not a matter of ability, but desire. They know people come to YouTube to be able to find whatever content they want. Content ID and their DMCA process is just paying lipservice to the idea that they are playing by the rules. They want this system. It keeps the new content churn high, which keeps users refreshing the page, which gets new ads served to them.
Then web services were invented, and now the law doesn't match up with how people typically use the internet. The laws need to be updated, and to do so we will have to fight against the Hollywood political lobby.
You see, the DMCA is a perfectly acceptable law if you were hosting videos on your own server. YOU would get the DMCA notice, and then you can decide whether or not you want to be held liable in court.
Today, you put your video on Youtube. Therefore: Youtube gets a DMCA notice, and Youtube administrators need to make the decision whether or not to go to court about the issue. The admins don't want to stick its neck out for millions of users using its servers for free, so they just comply with the DMCA notice and take down the video.
Its the reality of the current situation. If you're not paying for server space, you have no power. I'm not entirely sure that's a "bad" thing either, but I can admit that you can feel powerless as a user.