In contrast, you cant make a bank transaction without linking your identity. This is what people are talking about when they say blockchains give anonymity.
If someone cares about anonymity, that’s a huge gamble to make that the system will never have a design or implementation flaw (in the case of things like zcash which are, unlike bitcoin, attempting to provide anonymity at all), and that everyone they ever do business with is trustworthy.
That last part is guaranteed to be false. Beyond the obvious capabilities of a state-level attacker, think about why Equifax has that data in the first place. People will buy things on credit and that depends on not being anonymous – churning IDs would be like only paying cash for everything, which is known not to be viable for anyone who isn’t rich. Secondly, think about how many businesses want this data for marketing purposes: you can churn wallets all you want and it won’t help when the vendors are passing that information to companies like Acxiom, Equifax, or Google.