Yeah, I definitely like to see AI companies getting hit with their own medicine. The main problem isn't even "automated plagiarism": the pre-generative era was chock full of AI companies more or less stealing datasets. Clearview AI, for example, trained up its facial recognition technology on your Facebook photos, without asking for and without getting permission.
On the other hand, I genuinely hope copyright never "catches up", because...
1. It is a morally bankrupt system that does not adequately defend the interests of artists. Most artists do not own their own work; publishers demand copyright assignment or extremely broad exclusive licenses as a condition of publication. The bullies know to ask for all their lunch money, not just a couple bucks for themselves. Furthermore, copyright binds noncommercial actors the same as it does commercial ones, which means unconscionably large damage awards for just downloading a couple of songs.
2. The suggested ways to alter copyright to stop AI training would require dramatic expansions of copyright scope. Under current law, the only argument for the AI itself being infringing would be if it memorized training data. You would need to create a new ownership right in artistic styles or techniques. This would inflict unconscionable amounts of psychic and legal damage on all future creators: existing artists would be protected against AI, but no new art could be legally made unless it religiously hewed towards styles already in the public domain. We know this because music companies have already made their domain of copyright effectively work this way[0], and the result is endless bullshit lawsuits on people who write songs that merely "feel" too similar (e.g. Blurred Lines)
3. AI will still be capable of plagiarism. Most plagiarists are not just hoping the AI regurgitates training data, they are actively putting other people's work into the model to be modified. A lot of attention is paid to the sourcing of training data, because it's a weak spot. If we take the training data away then, presumably, there's no generative AI. However, people are working on licensed datasets and training AIs on them. Adobe has Firefly[1], hell even I've tried my hand at training from scratch on public domain images. Such models will still be perfectly capable of doing img2img or being finetuned and thus copying what you tell it to.
If we specifically want to regulate AI, then we need to pass laws that regulate AI, rather than just giving the music labels, movie studios, and book publishers even more power.
[0] Specifically through sampling rights and thin copyright.
[1] I do not consider Adobe Firefly to be ethical: they are training the AI on Adobe Stock images, and they claim this to be licensed because they updated the Adobe Stock agreement to have a license in it. Dropping a contractual roofie into stock photographers' drinks does not an ethical AI make.