Paying in cash, in addition to being a minor inconvenience that non-the-less outweighs most people's desire for privacy, does not work in online payments. It also doesn't work in businesses that get robbed.

The better question is, why do you need a new currency to get privacy? Why couldn't we have a private crypto currency backed by dollars or euros? There's no technical reason, indeed several groups are building this. What remains to be seen is if there's sufficient incentives to build anything around these or for any portion of the economy to move to them. Most purchases aren't sensitive, so for private payments to work, they need to be ubiquitous for non privacy reasons and just give people who need it the option for privacy. Much like cash does. But again, cash doesn't work online or increasingly offline