Fair use?

More than just a greed problem, it's mostly an age problem.

If you want to make money with anything related to culture, it's in your best interest to make sure everybody talks about your stuff. If internet users are allowed to see your stuff, talk about your stuff, make art and videos about your stuff, it will be shown to even more people in a virtuous cycle.

Ultimately this means more people buying your stuff and more money. It's fact that's something they could (and often do) pay for: it's especially indirect advertising.

The best example of that is the western video game industry. Technically, most companies could claim thousands of videos or shut down streams featuring their games but they never do. Because symbiosis is much more profitable than confrontation, you just make more money this way.

The reason Japan doesn't do that (or very reluctantly) isn't (just) because of greed. It's because Japan is populated, governed and managed by old people who think their marketing strategies from the 80s still work in a post-internet world. Stuff like deciding success or failure based on DVD sales, or only taking into account Japanese reception and ignore any global sales or acclaims.

Things are slowly changing, many creators are young and know how the internet work. But the old farts above them are the ones who ultimately have the money and decide how stuff is done.