Really? What's so special about strings? Perhaps I want computations to consume and produce trees. It seems like you've picked an arbitrary setting for computation and said "Look! My constructions which are naturally suited to this setting are naturally suited to this setting!".
So there's a real difference between various configurations of gas molecules in a box, and a real difference in the computational cost of representing them. Your statement is not unlike saying, "oh, so you've picked a high-entropy configuration, how convenient! What's so special about high entropy?" High entropy and low entropy aren't symmetrical. It takes more energy to move in one direction than the other.
Again, you shouldn't be surprised by this at all (I'd think it's rather obvious). Since typed formulations do proof work in their validation step (that can be Turing-complete in some cases), obviously that means that there is more complexity in their representation, otherwise, you'd have computation for free.
You can choose whatever representations you like. But representations that express more information, come at a higher computational cost.
I'm not sure why you think that I'm surprised, or even why you think that I disagree with your overall argument. I'm just trying to help you build your argument by pointing out the most obvious aspects which need more careful elucidation.
So your claim is that in the physical world strings are more fundamental than trees. Good to know. In fact I think there's an even simpler reason than the one you give of "entropy". That is, trees require space which grows exponentially in their depth, and thus they can't even be represented in the physical world.
A string is quite different from a stream. A string is typically considered random access, for a start.