Why not just have a per-site identity? In other words, tracking cookies become worthless because they can't follow you from site to site.
You have, in effect, described EFF's Privacy Badger addon. It works heuristically to block cookies from leaking from their original domains, except when told otherwise (some exceptions are included by default -- so-called yellowlist, check out "How does Privacy Badger work?" section). I've been using it for some time and seems to work very well with little breakage. Rarely have to whitelist something.