@Mr Bill would probably be one of the best people here to talk about using these - they were ideal for a large operation like a big portraiture chain.
Yes, the large chain lab where I worked initially had 4 VCNAs. Three were in constant use; one for each major "production" area. They were so critical to the operation that one was actually held in reserve as a spare. Even with a very expensive Kodak maintenance contract the spare machine was still seen as necessary. (It goes without saying that we did pretty high printing volume.)
These machines, as well as their successor, the PVAC (Pro Video Analyzing Computer, or something to that effect) were part of a manufacturing system.
The VCNA was essentially a sophisticated TV camera system looking at the color negative in the gate and displaying the result on a smallish CRT. There was also a lit area for a reference print. The operator would spin some large dials that were equivalent to changing cc filters in an enlarger as well as "density," which is loosely an exposure adjustment. The machine's display would show the anticipated print result. In a simplified system one might just write down the filter and exposure data, then manually set those into the printer (exposing machine). But one can probably see that this requires both the printing and processing machines to be held in very tight tolerances, and that these must somehow be "married" to the VCNA's setup.
In a say, 1980s implementation of a system, a mini-computer might have kept track of everything. We specifically used Nord package printers equipped with Lucht lamp houses (I roughly described their operation somewhere else on this site.) These lamp houses could automatically change exposure and filtration for each negative, much like a circa 1990s minilab machine. Essentially they used a set of three hard-cutting filters - cyan, magenta, and yellow. (Cyan filter terminates the red-light exposure, magenta filter terminates the green-light exposure, and yellow filter terminates the blue-light exposure.) Each filter is mounted in a "paddle" which is mounted to a rotary solenoid; this allows each filter to be rapidly flipped into the light path at the proper time, under electronic control. When the last filter comes into the light path all light is blocked (hypothetically) and a mechanical shutter is closed. By this means the computer can command any (equivalent) filter and exposure.
For the mechanics of setup one starts with a set of "printer setup negatives" on the specific film type. These include a known exposure series under a proper lighting setup, and correctly-processed film. The lab then makes a set of ideal prints from these with the printer being manually controlled. Adjustments are made until the over and under negatives all give matching prints, and the print data is recorded. The same set of negatives are put into the VCNA (or PVAC) and manually dialed to visually match the display. Now the system has a correlation between the visual appearance of the display vs the actual print exposure. It calculates a so-called "slope adjustment" which largely compensates for reciprocity failure in the print exposure, and is able to interpolate for any variation in the exposure. So the system is basically able to give a correct print exposure based on whatever one needs to dial in on the VCNA.
There is one small part missing from this. Obviously the VCNA system works for a single printer - the one it has been "married" to. But what about multiple printers? So Kodak also made so-called "translators," essentially a color-meter for printers, allowing a number of individual printers to be matched up.
As I said before, the VCNA/PVAC was part of a manufacturing system. Elaborate to set up and maintain. But incredibly capable in the right conditions. FWIW we saw ours as reliable only to within about 5 cc of color - not good enough for our work. So we always ran initial color tests before actually letting a long-roll of color film go to print.
Any pro-lab of decent size would have wanted a VCNA/PVAC (or the cheaper Bremson version, etc.). It all came down, pretty much, to how much time/labor one could save by eliminating one or two initial color tests. And again, it was necessary to keep pretty tight process control on things.