In discussions on the intrinsic value of BTC, one often reads the claim that BTC is scarce because the maximum amount of BTC that can ever exist is 21 million BTC. I find this explanation rather unsatisfactory.
If a group of people collectively decide to move all their savings into tulips, the price of tulips should skyrocket. However, new greenhouses could be built and some farmers could start growing tulips. As a result, the price of tulips would start falling and converging to the price prior to the "tulip mania". Seeing the value of their savings dropping, these disappointed tulip-lovers might rush to sell their tulips, causing the price of tulips to plummet. The media would then mock them for their financial illiteracy.
If the former tulip-lovers then decided to move their savings into gold, the price of gold would almost certainly rise suddenly. However, new gold reserves cannot be manufactured out of, say, lead — assuming that no form of working alchemy is developed, of course. Without the required increase in the supply of gold, the price of gold would stay "inflated" and there would be no panic-selling. A computer scientist would perhaps say that the supply of gold is rate-limited.
I know nothing about economics, but I suppose an economist would say something along the lines of "the supply of gold is much, much more price-inelastic than the supply of tulips". To me, BTC looks closer to digital gold than to digital tulips.
Questions — As a total novice, the scarcity pertaining to BTC I do see is in the rate at which new BTC can be generated. But, what exactly does that have to do with the number 21 million? When mentioning the total amount of Bitcoin that can ever be mined, shouldn't the practical upper bound on annual mining also be mentioned? Is my understanding of "Bitcoinomics" roughly accurate?