Agree re inverse square law. That works as a model only in space, when there is nothing like the ionosphere muddying the water. Even tropospheric bending and ducting on vhf and uhf fails to obey the inverse square law.
Your point about the increased power making the second (or subsequent) hop possible is a good one. Perhaps we should say that the second hop was always there but too far down below the noise (say, -36 db s:n) to be detected. The fourth and subsequent hops are there too but are too weak to be detected.
As you increase the power you should see a widening circle of receiving station start to detect the signal as it emerges above the minimum detectable by WSPR. With enough power you would see the skip zones narrowing too. You’d also see the third reflection start to become apparent etc. More power does increase the range but only in multiples of the skip distance.
The studies of propagation using wspr and low powered transmitters have demonstrated to mnay people the basics of propagation and that can only be a good thing.
What wspr has done is to allow receivers to look below the noise and observe signals that were always there but were not previously detectable. This would have been science fiction in past years. I’m looking forward to WSPR type detection getting 10 db more sensitive.
73 Andrew VK1DA/VK2UH