This is close but not quite right, I feel.
What is required is that a browser should automatically delete all cookies (and any other nasties it can think of) set by a domain as soon as the site is left; either by navigating to a new site or by closing the tab. A white list can exist to allow persistent cookies pertaining to login or other required data.
It should not be necessary to close the browser, particularly when the worst offenders are likely to be closed down pretty quickly anyway (say, by having found them through a search, had a quick look to discover it wasn't what you were seeking, and immediately backing out).