I wrote a Chrome extension to do what you describe, it breaks almost the entire web. I am experimenting with a generic rule set with a view of forking Chrome with a better default privacy and security policy.
I totally agree that users shouldn't need to know the details, but there are some things, like third-party cookies, that needs to be explained and simplified. A bit like not clicking on an exe email attachment.
I think the equivalent could be that users white-list websites, or 'install' them, if they trust them, which allows those sites to execute third-party cookies. Everything else would be 'incognito' by default.
But I am not entirely sure what would work, hence my experimentation at the moment. I know that the answer definitely isn't DNT.