The core issue is that the law is so laughably one-sided that sites effectively don’t have any other choice but ‘shoot first, ask questions only if challenged by someone with a loud enough voice’. You want to make stuff like this happen less all it would take is a few changes to the law:

-First and foremost, the copyright owner has all the responsibility, if they want to find infringement it it entirely on them, no more demanding that platforms do it for them.

-Next, institute penalties for bogus or fraudulent claims. If you’re going to demand that someone’s content be removed then you’d better be damned sure that you’re in the right, otherwise it will cost you. For this I would suggest breaking out an old copyright maximalist favorite that was making the rounds a few years back, the strikes system, and make it so that after a certain number of ‘strikes’ within a set period of time the content goes irrevocably into the public domain. If a person/company knows that making enough bogus claims will cost them the ability to make any claims related to that content in the future, as it will no longer be theirs, then they are going to be very careful in issuing claims, and unlike a monetary penalty this isn’t something a large company can just shrug off.

-Accusation is no longer treated as equivalent to a finding of guilt. Merely accusing someone of infringement should not warrant an automatic penalty as though they had been found guilty like removal of content, and if those issuing the accusations want to say that sites should be liable for facilitating infringement by ignoring claims then claims are not going to cut it, they need to prove that someone has been found guilty in court(default rulings wouldn’t count towards this) multiple times and the sites still did nothing.

-Along those lines I’d set up something like an anti-SLAPP law for copyright cases, where if the accused can make a compelling case that their use falls under fair use then the one who made the accusation is forced to, at a minimum, pay all of their legal fees. For obvious cases this dismissal and fee payment would take place at the outset, for less obvious cases it would trigger should they prevail in court. This would allow those that believe that they have a case but couldn’t afford it to defend themselves.

-Speaking of penalties, since the copyright maximalists love to compare copyright to theft the penalties should be scaled down to match, such that a song /movie/book doesn’t go from being worth a couple of bucks to thousands or tens of thousands simply because it wasn’t acquired/used legally. I imagine a lot of cases would simply never be bothered with if the potential payout was in the single, double, or maybe low triple digits, and since as far as I know that is the punishment for actual theft it would be entirely appropriate to set the penalties to that amount.

I’m sure there are refinements to be made and other fixes that could be added, but simply making it so that both sides face penalties for abuse and violations rather than just the one as it currently stands would likely go a long way to reducing those.