Note that I have not been printing a LOT, so my eyes cannot make the visual exposure and contrast determination that an experienced printer can do.
So for me, my enlarging meter is similar to a camera or handheld light meter when taking a photo. Except now rather than exposing film, I am exposing paper.
I use an old Unicolor meter that has a needle meter, and the meter is calibrated in f-stops.
1 - This gives me the ability to determine the approximate density range of the negative, which is a step in determining what grade to print at (as a starting point)
2 - After printing a GOOD print, I determine what meter reading a dark shadow is (almost blackest black on the print). The time will remain fixed.
2a - This allows me to get a close initial print exposure of another negative, by adjusting the f-stop to get that same meter reading.
2b - I can change the height of the enlarger head or change lenses, to get a larger/smaller print, and adjust the f-stop and the print 'should be' the same.
2c - I can also change enlargers, and given the other variables are stable, the print 'should be' the same.
2d - If I need more time to dodge, I close down 1 stop and double my exposure time.
As has been said, critical in this process is making that good "reference print" to base your exposure on. For this discussion, what method you use to make this reference print does not matter. What we want is the final exposure of the reference print. This is the reference exposure for that paper and grade.
What this does for me is with an unknown/new negative, is to get the initial print 'close.'
From that initial print, I will then evaluate the entire print to determine how to adjust/fine tune the exposure, contrast, and/or burn/dodge the print.
When I was taking a photo class at the local community college, the meter allowed me to switch between enlargers without a problem. In a school darkroom, you cannot "claim" a specific enlarger, it was "first come, first served." And I was not always first into the darkroom. I imagine the same scenario at a club or community darkroom, where you may not be able to claim or reserve a specific enlarger, you only have a choice of the enlargers that are not being used.
As an alternative to the meter, I also used the old Kodak Projection Print Scale (PPS), to print a 4x5 test strip. A pie shaped test exposure. This was just so much easier than the old fashioned test strip, As with the meter, the PPS only got me to an initial exposure. I still had to evaluate that initial print to determine what adjustments needed to be made.
If I changed the height of the enlarger, I would have to do it again. Although I could calculate the exposure change by the height change.
If I changed to a different enlarger the next class (remember in the school darkroom, it was "first come, first served"), I would have to do another test exposure with the PPS.
Where the PPS worked better than a meter was where there was significant general darkroom safelight illumination that could not be turned off. This could be the situation in a school, club or community darkroom. This general illumination could throw off the meter and give you bad readings (general illumination + enlarger light).
I have not used the Ilford enlarging meter, but I did get one to see how it works, and to see if/how I can use it in my workflow.
About test strips.
The method that I was taught in high school did not work very well, and it took me a LONG time to figure out why. A strip of paper was put down and a cardboard covered it. A series of fixed exposures of X seconds were used. After each exposure, the cardboard was moved to expose more paper. The problem was that each segment was a fixed X seconds more, not a half or full stop more. So I did not get the range of exposure that I thought I was getting. The exposure steps were getting smaller and smaller.
Example, using 5 second segments, you have 5, 10, 15, 20, 25, 30 second segments (6 segment to look at). But if you look at the exposure, from 5 to 10 you get +1x, from 10 to 15 you get +1/2x, from 15 to 20 you get +1/3x, from 20 to 25 you get +1/4x, from 25 to 30 you get +1/5x. If you were off on the upper end, where you needed more exposure, you could be way off. An f-stop exposure of 1-stop or +1x step for 6 segments would be 5, 10, 20, 40, 80, 160 seconds. Quite a difference from 5,10,15,20,25,30.
And where is the test strip placed? It is a strip that covers different parts of the image, which could have and usually does have different film density and may or may not include the main subject. It was no wonder that even with test strips, we had trouble nailing the exposure of a print.
I recently ran into an old test strip device. It had hinged panels, so you could expose 1 segment at a time. And because you could expose 1 segment at a time, you could easily make a f-stop scale test strip, exposing each segment for the specified time, independent of the exposure of the other segments. I tried to make an f-stop test strip by the moving cardboard method, but the math for the additional exposure of each segment was not easy to figure out, and I constantly made mistakes in the darkroom. And with the hinged test strip device, you could move the device to expose the SAME part of the image for each test segment. Now that was a test strip that made sense.
In the end, the darkroom enlarging meter (of various types), the Kodak Projection Print Scale, and test strips are simply tools. To use them you have to understand how they work, their capabilities and limitations, choose the appropriate tool for the job, and work within the capabilities and limitations of that tool. They don't replace the computer that is your brain, or the years of good printing experience, they only assist you in getting that initial print close.
. . . Sorry for being so long winded.