It is my model by the way (Burger refernences my post on Reddit so please give rigth attribution). It was my idea to plot log of price vs log of time.

Yes, it is unusual to do that but it makes complete sense because in doing so you are asking, how the price scales up in magnitude of 10, 100, 1000s? If you plot these changes in a log log graph and the relationship is obviously linear it means it takes times of 10, 100, 1000s to scale up similarly. That is what BTC does! What is weird or illogical about that? You are using your math completely wrong and you don't understand literally what you are doing.