If it were me, I'd like entire essentially unconnected sub-profiles, restricted by sites - different caches, potentially different extensions, etc. Even with third-party cookies disabled, you end up with little tricks to authenticate and track people across domains.
You mean like Chrome Profiles?
Firefox also has these kind of profiles, but he wrote restricted by site, so they'd have to transparently switch as you're using the browser.
No, because when you disable 3rd party cookies, then www.evilcorp.org can't even set its cookie on www.a.org.
So, mission accomplished?
I disabled 3rd party cookies ever since the option appeared in Firefox, and never had any issues.
I disable 3rd party cookies too, but I've had several websites that have failed to work properly because of it. So now I've had to whitelist certain 3rd party cookies (e.g. accounts.google.com, payments.google.com, etc.). But since these domains are whitelisted, they can set their cookies from any website I visit. With the idea rlpb proposed, each website (and its permitted 3rd party cookies) would at least be in its own container.
Disabling 3rd party cookies breaks functionality, e.g. tweetdeck.