At least for me, your definition is far too restricted and conflates the process with the objective that one might have.
For me, "flow profiling" is managing the flow rate through the bed of coffee as it is extracted.
One common objective
of using flow control is be to be able to "best" extract coffee from the bed
At its simplest, flow profiling is choosing an infusion method over a percolation method, selecting effectively zero flow, or some flow.
From there it can take many forms, as flow rate at a given point in time is related to the pressure across the bed and the bed's effective resistance at that moment. These may include all kinds of restrictors, such as gicleurs, E61 mushroom valves, needle valves on the supply side, valves on the exit side (such as a Clever dripper), filter paper in the basket, even the type of V60 filter paper, that change the overall hydraulic resistance to flow at a given supply pressure. One can also control the pressure or meter the flow. There are, no doubt, other methods as well.
These apply whether open- or closed-loop control is being used. If closed-loop control, how
you control the flow is much less important than what
If your objective is to be able to "best" extract coffee from the bed and you agree that
- The flow rate impacts extraction "quality"
- The pressure impacts extraction "quality"
then you need to acknowledge that, as there is a fixed relationship between pressure and flow at any instant in time, you can pick one to control and the other becomes a dependent output.
Pressure-driven control is familiar to many. It is how a typical pump-driven machine or a spring lever works, especially during the extraction phase. (There are certainly valid considerations around, for example, when the flow is restricted by a gigleur during PI.) A simple, pump-driven machine measures pressure at the OPV or bypass valve, and closes the loop at that point. A spring lever provides open-loop control, based on the spring rate and the position of the piston.
Flow-driven control has been practiced for decades, but not by that name. If you read the various manual-lever threads you'll hear over and over, "I ignore the gauge and just watch the stream, pressing harder or softer on the lever depending on what I see." This is closed-loop, flow-driven control. Agreed the accuracy of the flow measurement isn't to 1%, nor is the system response time to perturbations in the tenths of seconds, but it works.
Once you get into what is "better" for achieving a specific objective when that includes significant puck-to-puck variation, then there is a lot of testing to be done to determine what kinds of variations contribute most to preserving or destroying the result in the cup that you want.
There are some rough explorations that have suggested that, for many grinders, for espresso, somewhere around 1-2 ml/s during extraction tends to be commonly in the sweet spot for medium roasts. The "18 g, 1:2 ratio, in 25 seconds" suggestion can be thought of as a flow-rate suggestion. 36 g in the cup, less 3 g of extract is around 33 ml of water. 25 seconds less 7 seconds for ramp-up is around 18 seconds. 33/18 ~ 1.8 ml/s.
Similarly, if the pressure is extremely low (0-1 bar), you're making "drip", in the slightly higher range, something more akin to the original steam-driven caffe espresso. What many consider "espresso" seems to be associated with pressures in the 4-9 bar range. Somewhere above 9 bar, some find that the quality of the espresso diminishes in various ways.
Again, none of this should be a surprise. With a conventional, pump-driven machine or a spring lever, the barista chooses a grind and dose for a given coffee and setup that has a fixed, pressure profile during extraction to be able to achieve a flow rate that results in "best" extraction of that coffee for that pressure. With a manual lever or a flow-driven profile, the barista chooses a grind and dose for a given coffee and setup to be able to achieve a pressure that results in the "best" extraction of the coffee for that flow rate.