Trivially, cryptocurrency is less private than credit/debit cards, because every transaction is written to the public log. This is true of Bitcoin, Bitcoin Cash, Litecoin, and Ethereum.
Coin tumblers exist for all these currencies. But these a) cost a small fee, and b) are back to centralization, requiring you to trust the tumbler maintainers not to record the transactions.
ZCash[1] is the only cryptocurrency I know of which attempts to actually be private, but the unpopularity of ZCash relative to Bitcoin/Bitcoin Cash/Litecoin/Ethereum shows that most people involved in cryptocurrencies actually don't care about privacy.
But most crypto is anonymous, not private. It's usually worse than even banks since anyone can look up your transaction history given your wallet address. All it takes is one place where your wallet links to your identity and you have even less privacy than with banks.
Privacy is actually a common misconception when it comes to cryptocurrency. More currencies, bitcoin included, are actually the opposite of private – every transaction is completely public for everyone to see. There are currencies (i.e. Monero) that aim to add privacy, but by and large it doesn’t exist.
Zcash is not anonymous; cloaked transactions are optional and hardly anyone uses them (so they stick out like a sore thumb). It also requires trust that the founders aren't printing hidden coins (due to its flawed "trusted initialization" procedure used at the coins inception).
Monero/XMR is the only 100% private, fungible cryptocurrency. All transactions enforced private by default, with no option to send an un-private transaction.
Cash is private. Most cryptocoin are not particularly private. The few that set out to be private may or may not succeed at being private or being a widely exchanged digital currency.
How private are those then? Isn't it true that at least everything is visible to at least all participants?
EDIT: in other words, my question is actually whether your claim has relevance, considering how most crypto currencies aim to be public (or that's at least my impression).
What about zcash? As I understand it has much stronger privacy, but almost nobody understands it so people are skeptical. I'm surprised it doesn't get more attention.
Cryptocurrencies are terrible at privacy, too. Any time you try to use cryptocurrency to buy physical goods (or fiat currency), whoever you're transacting with can know every transaction you've ever made.
Coin tumblers exist for all these currencies. But these a) cost a small fee, and b) are back to centralization, requiring you to trust the tumbler maintainers not to record the transactions.
ZCash[1] is the only cryptocurrency I know of which attempts to actually be private, but the unpopularity of ZCash relative to Bitcoin/Bitcoin Cash/Litecoin/Ethereum shows that most people involved in cryptocurrencies actually don't care about privacy.
[1] https://z.cash/
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