The price of cryptocurrencies basically follows the rules of demand and supply. As the coin becomes scares it becomes more valuable and hence the price increases.
This is a very common fallacy that people repeat here year after year. It is not enough to be scarce to have value. An asset or coin in question should also have real utility, that is serve some purpose. If it is of no use to anyone, no matter how scarce it is, it will be worthless. In short, scarceness alone won't suffice. There may be some hype like in a pump&dump sequence but ultimately it all comes down to utility.
See 42Coin as one of the most conspicuous examples of just that. It now has a market cap of measly 122 BTC with a daily trading volume of 97 (sic) dollars despite all its scarceness, which pretty much says for itself. It is useless.