Except the law you compare it with is about stolen property, where an object is lost for the owner and so can be returned. The law you propose is about intellectual property, where no loss has happened and so the item will simply be destroyed, at no gain to anyone.
Also, again, stolen property is a very small part of the property on the market. Meanwhile items with unclear copyright is the absolute majority of the content of the internet. I'm not saying strictly pirated things here, but things where a private person can't be expected to know the copyright of.
And you still haven't addressed this.
By your idea every person who browses the internet would be a criminal just by the fact that their web browser caches the data, but lets assume all jurisdictions are savvy enough to ignore this (which we know they aren't from previous issues about cached data, but let's pretend.)
Okay, so now the number of criminals is limited to anyone who saves any information from the internet, ever, as well as anyone who ever reblogs or forwards pictures, and so on. So basically - the vast majority of people on the internet.
Oh, but they can avoid being criminals by only saving or sharing information where it's absolutely clear to them what the state of copyright is! Yes? Yes!
No. There is almost no such data on the internet. The best you can do is trust any copyright notices attached to the media, and given that these are typically just baked into the template of the site/blog/whatever, it's very rarely accurate. So pretty much all movement of media on the internet would have to seize in order to comply with your proposed law, which just isn't going to happen no matter how you twist it. It isn't reasonable, for one, and it isn't just.
Any law that makes everyone (or a vast majority) into criminals simply because they do not have a reasonable chance to know when they are breaking the law, is an unjust law, and a total no-go. Surely you must understand that?
Now can you actually propose an argument for how people are supposed to know the copyright state of the media they see in all countries that are affected? You sound like a perfectly reasonable person aside from the fact that you blindly refuse to address this simple and pivotal point that your entire proposal stand and falls on.