It's wild to me that anyone thinks that would be a reasonable law (whether or not it is law, I have no clue, I don't live in UK or EU).

If you made a website and you said "To view the private content on my website, you have to either pay me, or sign a name, any name you wish, in my guestbook" what business is it of the government to say "No, this random person refuses to pay or sign the book, but Thom, you have to let them see all your articles anyway."

Note that I used "sign any name" as the metaphor, not "show ID," since it is trivial to not allow any important information exchange if you simply delete the cookies yourself, which is easy to configure a browser to do. The end-user has the choice, if it's so important to them, to configure their browser. Even Chrome can be configured for which sites to allow cookies, which to disallow, and which to clear when the browser closes (the smart choice, since accepting them and throwing them away soon after is the undetectable option that accomplishes your main aim).