You aren't likely to convince me that one branch is more scarce than the others because I can see how big the whole tree is, and especially because I can see how many other trees are in the forest already.
(ETA: To make it clearer, you especially aren't going to convince me because I think Proof of Work is a waste of processing power. The real scarcity is processing power, and again, that's a political/economic game, that only props up artificial scarcity so far. Certainly not far enough that I trust the bitcoin tree to remain scarce in the long run. Not a question of if, but a question of when.)