Second, if you think that "simple tests of knowledge that signal larger things" is an important tool in vetting candidates then great, this question was very helpful for you. My opinion is that while citing rote memorized facts about names, etc. might be important for a contestant on Jeopardy it isn't a key attribute for the Presidency. I know that opinion differs from you on this and we'll leave it at that.
You are correct that rote memorization isn't important. But we aren't talking about rote memorization.
I can just picture this:
[Urgent Advisor] President Johnson, Putin has aimed his missiles at us.
[Gary] Who?
[Urgent Advisor] Putin is the leader of Russia.
[Gary] Where is that?
[Urgent Advisor] The northern portion of top of Eurasia.
[Gary] WTF?
[Urgent Advisor] We need to respond quickly.
[Gary] Are they our enemy?
Rote memorization isn't important. But damn you need to know about Aleppo, at least SOME foreign leaders, general knowledge of history, etc if you want to actually be able to lead in critical situations. The presidency isn't just about sitting back and thinking about your principles. It is about making crucial decisions in time of need. You have days to veto bills, weeks to write your speeches, you can ponder your principles then (and change parties/principles like Johnson did). But you can't take time to learn history in the heat of the moment.
If voters don't like Trump or Clinton. They still have Stein to vote for. At least she isn't that worthless Johnson.