The analogy also opens up another difference. In clojure, you often end up passing around a lot of maps with string keys. What are those keys exactly? You have to crack open the clay brick to take a look at how it works. With the stick model, you can often see how the sticks work if the bundle of sticks has been color coded nicely - eg, well constructed generics. Luckily cracking open a Clojure brick is as simple as ctrl-clicking, so it's not nearly as bad as it sounds!
Programming parables are definitely weird though - programming does not have true analogies with the real world. It's more of a superset of the real world and the use of programming languages is more akin to defining physical laws than building bridges with clay or sticks. I don't think we as humans have really come to understand exactly what we are unlocking with the development of programming and how vast it really is.