No, most so called "cryptocurrencies" are using lottery-based Proof-of-Work (puzzle solving) as a leader election mechanism for Byzantine consensus over the st

No, most so called "cryptocurrencies" are using lottery-based Proof-of-Work (puzzle solving) as a leader election mechanism for Byzantine consensus over the state of the distributed replicated ledger of transactions. What described here is a simple probabilistic micropayments. Since the payment transactions are expensive, you amortize the cost of many smaller "virtual" transactions over a single large real transaction. This scheme is frequently used in the API billing, or even for all-inclusive costs in hotels (i.e. you charge for the buffet instead of for each meal separately) and you hope that probabilistically it will end up OK.