Is open (as opposed to private) finance fundamentally cheaper for the participants?

Let’s say I send some money in an ideal crypto universe. Do have to pay a premium to make the transaction private, or will their costs be equivalent once cryptocurrency tech evolves far enough?

I am familiar with the various options for private transactions in cryptocurrency. What I am interested in learning is whether, in the long run, most transactions worldwide will likely be openly accessible. Of course private transactions will still occur even if they are at a relative premium.

The implications of this on the global economy would be really interesting if so! Imagine being able to see a substantial portion of the global economy’s money flows as freely as seeing information on the internet.