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?
It may be that. I just tried and Twitter is working perfectly without third-party cookies. Some months ago it didn't allow me to login.
With Google I had a similar problem, I couldn't login into my Google Account in sites that weren't the search engine (Docs, YouTube, etc). I just tried them, and again, it seems that it works now.
I use Chrome stable. Maybe something changed in the management of third-party cookies in recent releases?
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.