As we see with the adoption of credit and debit cards, mobile billing, and things like ApplePay, most people don't mind having their transactions recorded. Indeed, for a lot of people it's a benefit; I avoid paying with cash so that I can easily use things like Mint to have a better understanding of my spending.
Criminals, on the other hand, strongly value secrecy over convenience, and tracking money is one of the best ways to keep crime in check. So unless you find some way to eliminate crime, being secretive about money flows will always put you in company with criminals.
IMHO, lack of anti-crime controls was one of Bitcoin's biggest early mistakes. It was much worse for, say, buying a book online. But it was much better for crime, including digital extortion and fraud. It quickly picked up a taint that it's never really been able to shake. Let that be a lesson to startup founders everywhere: your early adopters can easily define your company.