I generally find it much more intuitive to think of pressure as the result of flow, than the other way around. In fact, you’ll notice the Hagen-Poiseuille equation (and most other flow equations) are typically given with pressure drop as the dependent variable (and flowrate or velocity independent).
An analogy is driving a car - would you say that your speed increases proportional to the drag force, or that the drag force is proportional to your speed?
Pressure drop down a tube can be thought of in much the same way - resistance to flow as the result of friction (i.e. drag)*. The greater the resistance, the greater the pressure drop for a given flowrate. In an espresso machine, it is the pressure drop that determines the backpressure at the pump (i.e. the pump discharge pressure).
I personally think the emphasis on pressure in espresso has overshadowed the importance of flowrate/velocity, and wonder if the “flow depends on pressure” perspective is part of the reason why.
*That’s a really simplified model, and it’s always important to remember that all models are wrong, but it’s certainly much more useful than the ubiquitous garden/fire hose analogies (which just lead people down the garden path).
@latte911 - interesting info in that guide from La Marzocco. Rather round numbers for the flowrates with the various different gicular sizes. Comparison with (predicted) pressure drop across just the gicular (i.e. excluding the rest of the system) is interesting: