Actually, an inclined manometer is still one of the most precise ways to measure flow. The principles involving Total Pressure, Static Pressure, and Velocity Pressure are self-evident by the physical representation of the manometer. So, it is an unparalleled teaching tool.
I agree that its value in the field is limited. Although, its use in precision applications is not uncommon, and spying an inclined manometer fastened to the side of a duct or air movement device is not a singular event.
The problem in measuring flow directly exists with every instrument, including the manometer: the velocity field. Friction and turbulence are a reality in every instance. At best, the velocity field may be laminar with some small fall off at the edges of a duct. Regardless, methods to measure this field are well documented: a duct traversal is performed and a sampling grid over the cross-sectional duct area is created. This is fine for field measurements with a handheld instrument, but what about for permanent control?
Often, elaborate annubars or circular flow rings are used to sample the flow field with statistically-leveling multiple sample points. However, turbulence still leads to some unreliability and inaccuracy. To limit this error, straight distances of undisturbed flow are required before and after the sampling grid location. This puts a limit on location flexibility, and the devices become structurally inconvenient. All of this adds cost. Further, ducts may have particle contaminants. Even dust can affect readings. Some mfrs developed positive pressure annular annubars for industrial processes, but I have even seen these type clog up.
The most reliable method of control is pressure - specifically, the measurement of static pressure. Pressure sensors are reliable, precise, and cheap. Once flows are established through Test and Balancing (measurement), static pressure becomes a reliable indicator of flow - depending on the rating of the fan. However, even if flow vs. velocity varies, the static pressure remains a reliable control of fan performance. Some applications combine documented ratings with a static pressure sensor and current measurements on the fan power. That nails it pretty good for a tight, closed control loop.