If it is as simply as that, many shitcoins can shoot up in price and you know shitcoins don't have price soar like this but their projects died, price plummeted to zero, trading volume is non existent.

Demand and supply principle works but it is not affected only by scracity.

The YEARN finance token YFI has only 36.64k tokens in total supply and about scarcity, it is actually is scarcer than bitcoins.
https://coinmarketcap.com/currencies/yearn-finance/

You see that its token price can not soar to the moon and this token is an example that only scarcity can not help to build up value or price.