The DMCA is totally broken, and has been from the beginning. There are no consequences for anyone making a fake claim. However there are severe consequences for someone who receives one and doesn't take action. There are counter-claims processes, but that puts a heavy burden on both the creator and the platform.
I myself am guilty of abusing the DMCA. When I was fighting fraud for eBay and PayPal, if we found someone hosting a phishing site, we would use the DMCA to get them to take it down, claiming they were violating the copyright of the logo. We would send DMCA notices to any host in any country. Most would just oblige. A few would reply and inform us they weren't in the USA.
But it worked because the platforms feared the consequences of not following it, and there was no risk to us.
The DMCA needs fixing by adding severe consequences for incorrect use.