> Plus my understanding is that these ledgers do not scale. Each transaction takes a lot of computing power.

This is a particularly gross distortion of reality by people who for whatever reason want people to believe cryptographic currencies won't scale.

In the infancy of a currency, when there aren't many transactions, the mining power amortized over each transaction will be much more than when many transactions are happening. Each transaction doesn't take mining power, the number of transactions and mining are completely decoupled.