[johnbuckman]

The problem is that your mental model of how a boiler based espresso machine works is not how they are actually wired.

Here is how they actually work: 9 bar of pressure are generated between the pump and a flow constrictor which is placed before the boiler, pumping cold water into the boiler. This cold water then displaces the water in the boiler, which then gets pushed to the espresso.

Thus, the final pressure depends on the compressibility of the steam (or airspace) in the boiler. In practice, you get about half a bar less at the espresso than the pump got behind the boiler. But, the real numbers depends on lots of factors, many of which are invisible.