While i generally think this is an interesting point of view, there seems to be one huge flaw with this logic.
To mine gold you need a somehow fixed amount of effort.
The effort to mine bitcoin instead is dependent from the amount of people trying to mine bitcoin.
Higher price of bitcoin -> more people mining -> higher difficulty -> higher cost of hardware -> higher price of bitcoin -> repeat
It is more likely it's the other way around: price of bitcoin dictates how much effort and money people put into it.