If talk about bitcoin, miners need to get a hashing result. The faster they can do hashing, the more likely you mine the coin. The mining difficulty increase, thats why bitcoin is power hungry.
However this is the first cryptocurrency from over a decade ago, there are many other cryptocurrencies snd I don’t think this generalization holds true
Your answer is in bitcoin.org/bitcoin.pdf document. There is so-called Time Server which is needed for constant number of blocks to be produced while number of miners might be any. So, it is not the cryptocurrency is power hungry, but users.
Oh, and the game resets every 10 minutes, where I'll give away the same prize again. For 4 years total, then I half the prize.
Go.