How would this be better than what we have now? If the answer is "cryptocurrency increases in value," I can assure you that's a terrible reason. Cryptocurrency is slower than card networks. It's more expensive than practically any other way of sending money. And as far as scale goes, it would need to become orders of magnitude more efficient to handle even a small percentage of consumer transactions. After all, what'…
Not inherently. If you compare apples to apples, accepting a credit card transaction is equivalent to accepting a zero-confirmation cryptocurrency transaction, which is just as fast as a CC charge (instantaneous.) And it is technically safer for a merchant to accept a 0-conf crypto tx because a CC charge is trivial to reverse (via a fraudulent chargeback) while a tx in the mempool of thousands of nodes is typically (not always!) hard to make disappear.
«It's more expensive than practically any other way of sending money»
Far from true. Average remittance fees are around $7 per $100 sent. Meanwhile Ethereum has fees typically under $0.50 per tx: https://bitinfocharts.com/comparison/ethereum-transactionfee... Of course there are periods of fee surges (over $5 per tx!), but it's not common.
«a full record of every monetary transaction performed with such a currency»
That's technically not needed. There have been proposals to implement what we call UTXO commitment sets, which is basically a way to revamp a blockchain so that it can discard old transactions and just keep track of current balances. (This is different, but roughly the same principle as "pruning.")