It could be that this technique favors people good at telling stories.
Personally, I'm a horrible storyteller. If you were to ask me what I did over the weekend, I'll offer some facts like "oh, went swimming in a river and Bob lost his hat, but we found it later. The water was nice." Whereas Bob could easily regale you with stories about the epic hunt for his hat and throw in a punchline in the end.
If I didn't know that you'd be asking for solutions I'm proud of, I might draw a blank at that moment. Granted it's an interview setting and these are the questions one needs to prepare for. But if given the choice between speaking about myself or whiteboarding, I'll take the whiteboard.
I've always preferred math over history for that matter. It's easier for some of us to apply processes than to recite chronologies.