The rules are already different for humans and machines. If I memorise a copyrighted book then that’s not copyright infringement, but if I store a copy on a hard drive then that is. You ask why distinguishing between humans and machines matters and then answer your own question: “we end up in a dark place”.
IANAL, but as I understand it, the difference is because copyright is about the transmission of the work.
If you memorize a work, you have used the work in accordance with copyright law: you were authorized to read the work. If you write out a copy of the work you memorized and give it to someone, you've broken copyright law.
If you store a copy of a work you were authorized to have, you have not broken copyright. However, if you download a book that you have no authorization for, that is a violation of copyright.
In other words, it's not about where the work is "stored" or whether or not humans were involved, it's about the transmission of that work between parties.
