The anthrax attacks in the fall of 2001 brought to light a number of uncertainties about how to tell whether a building is clean enough to re-occupy (How effective is sampling? What's the anthrax dose-response curve look like? What's the distribution of spores in a building?, etc.).
As part of his investigation, a colleague of mine constructed the nomograph in this paper, to illustrate the tradeoffs involved. By presenting the uncertainties graphically, the nomograph helps visualize the tradespace, in a way that simply running multiple numerical calculations won't necessarily do.
By the way, this also shows that these are not an entirely lost art.
For example, a power plant is littered with sensors, reading various pressures, temperatures, valve settings, etc. The traditional interfaces—a dial for every value, as per Three Mile Island—does not help a human operator in understanding the relationships in the data. Today, interfaces are designed to better explain how different parts of a system interact, and a nomograph can help an operator build a better mental model of how a change in a series of inputs affects an output.
A simple calculation on a computer can produce all of the numbers defining the operating point of a turbine, but a good nomograph will convey the physical relationships of the system.
I realize these types of displays aren't seen by most people on a regular basis, but they're far from irrelevant.
But that is a plot of data, not an analog computing method on paper. You can simply improve the presentation or organization on data. I suppose operators have computers nowadays :-).
This has advantages for someone trying to understand a system over both symbolic equation representations, which are very abstract, and cartesian type graphs, which often are not good at plotting more than one or two variables at once.
I agree with you that with fast interactive computers it's possible to come up with other possibly better kinds of graphical representations, but the creators of those can still learn a lot from the design of nomograms.
They also could be really helpful to teach graphic learners about how certain relationships work -- I am certain I would have understood many concepts much faster with one of these -- particularly in physics.