Sometimes trivial accuracy is all it takes. We just went through a battery replacement followed by an alternator replacement (the real problem) [...] We certainly won't be using my Fluke 189 to work on a car.
Considering your annecdote... I'm wondering if the symptom that you replaced a battery when the alternator was the problem wasn't from the cause you didn't want to use a good tool for the job?
I wasn't involved in the troubleshooting until the new battery failed the day after it was replaced. That's the whole point of the educational opportunity. I KNOW how to troubleshoot electrical systems, my grandson does not. It would be nice to transfer some of my experiences while I am still around.
I only need a couple of numbers off of the meter. Somewhere around 12.6V when I walk up to the car and the battery is charged. If it is much less, there's an issue. Somewhere around 13.8V when the alternator is turning (battery charged) and it probably works. If I only get 12.6V or less when the engine is running, the alternator is toast. Turn on the headlights and watch the battery voltage for a few minutes...
So, I just walked out to my truck and the battery measured 12.2V. Fine! It hasn't been driven in a week, I wouldn't expect it to be fully charged. I started the engine and got 15.1V. Again, fine! It is charging the battery that we already know is a bit low. Done!
One other useful measurement that is easier done with an analog meter is to watch the battery voltage when the engine is cranking. If it drops much below 10V, there is some kind of high internal resistance. I have seen batteries that appear to be perfectly charged be totally incapable of cranking an engine.
None of these measurements require even 3.5 digits. A $6 Harbor Freight meter is entirely adequate. I cheated and used my spiffy new EEVBlog meter but it certainly wasn't necessary.