I'm not saying your idea sucks, I just find it to be similar to cookies, with the cookie ID in the URL.
If UniqueThing is the only way for the website to identify me, many websites will add any additional information they gather about me to this ID (e.g. my email address when I subscribe to notifications). Currently, when I share a link, I just copy and paste the URL from the browser's address line. If I happen to share a personalised link -- willingly or by mistake -- my preferences and collected information will be available to all visitors of said link. If some of these visitors like the site, they will change the preferences and add red sandals, vampire books, and "herbal remedies" to the already existing Python books and science fiction. Now I can go in there and reset the preferences to my desires, but some of the people I shared my link with will come back and add whatever it is that they prefer. I'll have to create a new UniqueThing. (Which is similar to purging my browser's cookies.)
I like your Amazon example, this is something that happens to my wife and me, too. It would be great if Amazon could distinguish between the two of us; after all, although we share an account we're using different browser sessions and different laptops. Maybe we could think of a way to voluntarily inform websites about some of our interests. In the browser's settings, let me define keywords or select from a list of categories, and when the website I'm currently on sends a specific request (with the possibility for me to whitelist/blacklist any site), let them know about my preferences.
I use ad blocking, ScriptSafe and Ghostery, different browser profiles for various environments and needs (home, work, google, whatever). I don't click on ads. But I wouldn't mind if my browser informed any website that asked that I'm interested in Python, electronic components, and Stuart MacBride books. This would allow them to collect information about their audience's interests and adapt accordingly. It would allow Amazon to differentiate the shopping experience for my wife and me. Of course this would make some people more identifiable because of their unique interests, but browser-fingerprinting is already quite good at that.
I'm not claiming that my idea is better, just brainstorming here.