Thanks for reading and for your reply. At first that is what I thought too. Obviously we do not know for sure unless/until this design is tried in the real world.

However, on further reflection, it does not seem so clear cut. If you imagine that the sharechain has some notable featureset that people want to use, then it is reasonable to expect the price to be (perhaps barely) positive. Additionally, since the sharechain has its own difficulty adjustment, it seems natural to think that some sort of price/difficulty equilibrium would be reached.