I think it is related to Benford's law in that they are both a manifestation of the fact that a log scale is the most natural (most uninformative, highest entropy) distribution (or prior) for things that have magnitude (having a parameter that can't go into the negatives such as height or length or volume as opposed to a positional parameter which can be negative).
I do believe this is a property of the universe and not just a psychological phenomenon. Our mind here is simply following the natural distribution and Benford's law is just the observed manifestation of this pattern.
This type of pattern is not odd if you are believer in the Bayesian interpretation of probability theory. The shape of Benford's distribution follows the shape of a maximum entropy, most uninformative distributions for a value of magnitude (as I mentioned, positions do not follow benford's law).
Take street lengths for example. Assuming that they follow a log prior simply means that for a length of street L, if you pick another random street, you are as likely to pick a street within the length range L/2 to L than L to 2*L. From the original street length, to get a street twice as short, you need to subtract much less than you would have to add to get a street twice as long. That is why this distribution is not linear or rather it is linear on the multiplication and division operation, not on additions or subtractions.
If instead you'd assume that a street x meter longer is as likely as a street x meter shorter you would end up with impossible probabilities. For example, for a street of 1 km, a 3 kilometer street would be as likely as a -1km street? Even if you'd assume probabilities were equal for all lengths between 0 and infinity that would mean you think there are as many streets measuring a tredecillion billion km long as there are street 5 km long. This is simply not how things are sized in the universe. Smaller things are in greater numbers. Log priors are one of these areas where the math predicts the universe logically and the universe is mirrored by the math beautifully iff you do your calculations properly (using Bayesianity). It seems evolution has made our psychology reflect this reality.
I don't think Benford's law has anything to do with human psychology, it's more of mathematical property that applies to random sample from certain distributions.
