The thing that is rare is the total amount of mining nodes behind bitcoin. That is what you are buying into, is mindshare. Of course the mining nodes are mostly profit driven. If another coin had a higher profit margin, the miners would switch over to that coin.
That rarity too is also software controlled based on the difficulty curve. Bitcoin doesn't have to boil the oceans, it could make mining easy enough again that transactions could be mined in a coffee break on an average person's smart phone's GPU.
As I said, the scarcity of Bitcoin is much more a political structure than an inherent nature of Bitcoin. The miners control Bitcoin so much as anyone does and it is their political intent as much as anything else that creates any scarcity in Bitcoin at all.
