I doubt the movie industry would have died regardless of what form copy devices took. But to address the VHS/Betamax question, the answer is copy degradation. Video tape is an analog media. A copy loses a bit of definition. Every generation of copy from a master gets worse and worse nosier and grainier. The movie industry did like video to be copyable, but after the Sony Betmax SCOTUS decision, they could live with it.
That all changed when "they" introduced the CD and DVD formats. Those are digital. Unlike analog mediea every copy of a digital data is perfect. It doesn't matter how many generation a copy is removed from the source master. It's just as pristine as the original source.
At first it wasn't any problems so they though. Initial costs of the equipment players and especially duplicators may them limited their spread. But when duplicators/copies/burners became prevently, "they" throught their control of the copy media was enough. The sector of a CD which determined their type (i.e. Audio or Data CD) wasn't accessible via a CD burner. Burn an Audio CD, you have to pay "us". And the DVD keys section which video DVDs depend on was off limits as well. So no duplicated DVDs won't play on a player. And their draconian licensing terms ensured that the critical keys are kept off limits. And their walled garden was supposed to keep things looked away. But their wall garden had a dual weaknesses:. their lousy encryption scheme and PC CD/DVD burners and software players.
Technology kept advancing and even traveled around the CD Audio wall. Read the audio tracks as data and play back the data via software. And we all know the story about DVD Videos. A sloppy software player left their key inside. First new software players used that key. The it was found the encryption scheme was weak and it was eventually broken. and ultimately DeCSS.
As others have pointed out. the ultimate problem with copy protection is that it eventually has to be read/viewed/heard by us humans in the analog realm. And things can't be tied to having 'Net access all of the time. So that means they they have to give out the keys that go with the locks they have. It doesn't matter, as this HDCP kerfluffle illustrates, how convoluted you make the unlock process. The end users have the keys. And if I have the keys, I can easily open the locks.
In the end, the downfall of the music industry giants is them failing to adapted to the new reality, and them trying to enforce the old regimes. They days as the gateways of music is over. Technology and the Internet has open the world to budding musicians.
And I think that the movie industry gaints are coming to a similar reality as well. Technology especially in the realm of CGI is advancing at a breakneck pace. It's getting better and cheaper all of the time. The tools are available to everyone. And even the renders are becoming photorealistic. I've seen CGI people that make me think they are real. I've have to second look to make sure they are CGI. And huge studios and sets no longer needed. Bluescreen/greenscreening can put actors into any place imaginable. A lot of fan films are making huge strides in their production values. They are reaching the levels of exceeding the B movies I've seen.