The entire point of the Digital Millenium Copyright Act (DMCA) is to prevent companies from having to sue you to take your content down. So you're quite correct that nobody is getting sued over these claims. In the grand scheme of law in relation to copyright infringement, putting a song online along with a video is a pretty innocuous infringement.
The problem is that YouTube itself has been sued by copyright owners. And in order to deflect those lawsuits, they have developed systems that protect the copyright owner and YouTube, at the expense of the user.
That's why it is important to know what your legal rights are. If you know that you have a really solid fair use defense for a piece of content, then you can dispute and appeal these claims with full confidence that you will win, eventually and not lose your channel or have other sanctions in the process.