I routinely run with only direct cookies permitted (no third party ones) and with all cookies except those I have explicitly whitelisted being deleted each time my browser is closed.
I am not aware of any problem this has caused me for a long time, including on the sites you mentioned. Maybe there is some useful feature I'm not seeing at all because of the cookie restrictions I impose, but maybe they've just got better over time at not relying on cookies for things they shouldn't?
Safari help says "Select to reject cookies from advertisers and from “third parties”—websites other than those you open. This might help prevent certain advertisers from storing cookies on your computer."
This might mean that they reject third-party cookies from being set, but not from being read. That is, once you get a cookie (e.g. signed in to Facebook), every other request to Facebook (even if it's through the "Like" button) will also send your cookie.
The flag that appeared in the latest Chrome beta specifically disables sending of cookies to third parties, even if you have them.