It would break some sites (certainly not every site, I'm browsing this site right now with it enabled) because 3rd party cookies are an entrenched, standardized feature of the web, you can't simply turn them off tomorrow. Developers are using them to create benign functionality, for example spread an application across multiple domains owned by the same publisher.
What I proposed above is that we introduce an opt-in feature: before the browser is allowed to connect to 3rd parties (in the tracking and cookie sense), the user needs to opt-in, for example by clicking in a notice window displayed at the corner of the browser window. Instead of nagging every user of every site that "This site is using cookies", developers should nag only when connecting to other applications, using a standardized browser API. After sometime from standardization, you can roll out this functionality to all users and nothing legitimate would break.
There should be no presumed used consent - because there really is none, the outcry against Facebook and advertiser tracking shows people don't expect the web to work the way it does.