“Global food chains” have lots of strategic depth. When you see a crisis somewhere affecting those and causing famine, that’s usually for the regulation time, not until the crisis itself is resolved, and scaled accordingly, not on the scale of the crisis itself.
Most of the agriculture on our planet works inefficiently. Such an event, if we accept your scale, would just ultimately destroy the producers who do that in favor of those with modern effective means like intensive gardens etc, like many in Israel or Netherlands.
Now, this surely is going to give power to people we maybe don’t want to have it. But this doesn’t mean 6 bln people dying.
EDIT: Forgot to say - climate change is not something which would happen in an instant, so it’s going to be regulated more efficiently than, say, crises caused by wars and revolutions.