I've found that intuitive explanations for relatively complex things are generally easier than a long, exact explanation.

Certainly easier, but don't give comparable depth of understanding or justify comparable certainty in statements about the subject matter. Also, the dichotomy is false, since detailed explanations are ideally accompanied by intuitive explanations to improve understanding.

What we were talking about instead is when you have only a fast informal explanation, without the detail.

If you listen to the way that researchers talk, it's basically analogies and toy problems, with occasional black-board sessions if they're mathy.

It's because they already have the rigor down. See this post by Terence Tao.