It breaks things like "sign-in with github credentials" in CIs. But you know, these should be exceptional, therefore the default should be to load third-party content without cookies. The problem is that some content is loaded without your having to click on something (where you'd have a chance to right-click and request loading with selected credentials).
Not necessarily: OAuth Basic Flow does not require third-party cookies. With Basic Flow, you'd get redirected to github.com, making it a first party request. Github will then redirect you back passing an authentication code as a URL parameter.
I use uMatrix for this purpose, and to block third-party frames to defend against clickjacking. That said, Multi-Account Containers still are very useful.
