In wireless communications, is it true to say: The more the range, the more the delay spread?

The general idea which can be drawn by reviewing wireless channel models says that the longer the range/distance, the more the delay spread, even in LOS microwave links. But I really wonder why it is true because by simple geometry, supposing a fixed environment like the following figure, the opposite seems true ($$\tau_{2} / \tau_{1} \propto d_1 / d_2$$) Is that because the more the range, the more the needed power, and therefore, a new environment which in this new environment, the more delay spread is more probable? Thanks!