> Somehow, natural languages appear to fit somewhere in the middle.

I don't recall where, but I have heard an argument that there is pressure on the information density of natural language, as follows: If you are frequently misunderstood, then you can save effort (not have to repeat/explain) by adding redundancy. If you are never misunderstood, then you can save effort by removing redundancy.

There's no particular reason the result of this process should be good for crosswords, but it's a reason to be in the middle rather than at the extremes.