Well, the law does not allow YouTube to "punish" false DMCA takedowns, so in those cases there's not much they can do. It's up to the person who had their content taken down to file a lawsuit if they want the person filing the takedown notice to face punishment (which is one of the broken aspects of the DMCA law).
YouTube does punishes false claims through their Content ID system, though, as that's a system they control. From their website, "Content owners who repeatedly make erroneous claims can have their Content ID access disabled and their partnership with YouTube terminated."
YouTube says that, I've seen no evidence that they've ever actually punished a false claim, or even prevented that false claim from happening again.
For example, a video of mine was ContentID claimed for a public domain piece of classical music. I successfully contested the claim (the scammers give up quickly because their bread-and-butter is the 95% of victims who YouTube scared away from the "contest claim" button, or who never revisit the video page after posting). About a month later, I re-edited the same video and re-uploaded it, and I got the same fraudulent strike from the same scammer that I'd already successfully contested.
Yes, it's one of the major issues with Youtube right now, even with then putting funds into escrow. It's also an opportunity to have fun, such as people uploading videos to deliberately trigger DMCA claims from multiple parties so that they can fight over it.
Not if there were simple measures put in place to stop new or otherwise unused accounts from making copyright complaints. Just to be thorough there could be an outlet for unregistered users that had a higher threshold of evidence required before taking the alleged infringing video down.
Kind of funny how it takes more effort to earn the privilege of downvoting on hn than it takes to make a legal statement (perjury yada yada) but I imagine adding these constraints will lead to a lawsuit before you can spell class action. Even if the lawsuit ultimately fails, it costs a bunch to defend it. In the face of effective zero competition, how can they justify the expense/risk to their corporate owners?