I would emphasize that people who are good at mental math tend to not see a chalkboard, while those are less good at it tend to. Relying on visualization is, I have noticed from asking around, a weakness. Of course it's just anecdotal but the pattern seems pretty pronounced to me. (I polled a hundred people at one point and saw this pattern reflected in the responses)

I agree, though, that visualization is probably latent even in people who can't do it. I notice it when half asleep for instance.