As a student in physics, I always used to joke about how we should say "3 megadollars" and "5 gigadollars" instead of "3 million dollars" and "5 billion dollars".
I think it would help if news reports always used the same units. "This project would cost 0.1 Gigabux out of a total agency budget of 18 Gigabux." Switching between millions and billions and trillions can obscure how small, or large, something actually is in relation to the whole.
There are three major reasons why Tarsnap pricing is defined in terms of picodollars per byte rather than dollars per gigabyte:
Tarsnap's author is a geek. Applying SI prefixes to non-SI units is a geeky thing to do.
If prices were listed in dollars per GB instead of picodollars per byte, it would be harder to avoid the what-is-a-GB confusion (a GB is 10^9 bytes, but some people don't understand SI prefixes). Picodollars are perfectly clear — nobody is going to think that a picodollar is 2^(-40) dollars.
Specifying prices in picodollars reinforces the point that if you have very small backups, you can pay very small amounts. Unlike some people, I don't believe in rounding up to $0.01 — the Tarsnap accounting code keeps track of everything in attodollars and when it internally converts storage prices from picodollars per month to attodollars per day it rounds the prices down.