Earlier quoted context omitted.
In practice, User-Agent strings (which are just HTTP headers) have been shown to be pretty effective at uniquely identifying and tracking most people. So even disabling JavaScript and Cookies only goes so far.
Source? Because the only information contained in user-agent strings in modern browsers are browser version (realistically limited to vendor since browsers auto-update) and operating system version. So basically all you're going to get is (Chrome/Firefox/Edge/Internet Explorer/Safari on Windows/Linux/Mac), which isn't much.
Example:
Mozilla/5.0 (iPad; U; CPU OS 3_2_1 like Mac OS X; en-us) AppleWebKit/531.21.10 (KHTML, like Gecko) Mobile/7B405