I'm going to propose a more radical fix: we need to stop letting the DOM have reliable access to so damn much information.
When we started the move away from webpages and toward web applications, we let the DOM have access to pretty much everything, because applications are big and general and data-hungry: The DOM captures keystrokes so each website can have it's own controls and hotkeys (and which unintentionally lets a user be identified by keystroke dynamics). The DOM has access to blocks of offline memory so that applications can be stable offline or when infrequently connected (and which is another vector for super-cookie tracking). It has access to viewports and peripherals for responsive layouts (which is more data for a browser signature that can easily allow user activity to be correlated). CSS needs read access to layout colors if it's going to be changing them dynamically (which means that those colored as recently-visited by the browser are know, which allows for history-based signatures).
The DOM has demanded every piece of data available to the browser in the name of ever more byzantine applications, even though all but an insignificant portion of the web is still consumed in a page-like way. You can use NoScript and set Opera/Firefox/Chrome preferences until your blue in the face, but you will never reduce your tracking cross-section while the standards bodies insist on pushing these very broad, demanding features in the standards themselves.