Late to the party but I'll add my two cents worth.
I did my apprenticeship counting turns, marking dials with grease pencils, setting up indicators for final depths, blah blah blah etc. Been there done that. Though I got out of the machining trade, when I bought my first home shop mill an lathe 20 years ago I installed a DRO and have never looked back. Much less chance for error, setups are quicker, parts are easier and quicker to produce.
I don't sneak up on finish cuts. I do an initial cut at my finish depth and feed / speed, measure and set the DRO. Rough at whatever the machine / material will handle and do my finish pass at the same depth I set the DRO. Never had a problem hitting the same number within a few tenths.
To me that art of machining is figuring out the most efficient and/or cost effective way hold and make a part. What steps, tools, jigs, fixtures and in what order. Cranking handles is the easy part.
Now for the pure hobbyist who enjoys the full experience of manual machining and just working on a machine and doesn't have the desire for more modern systems I say go for it.
As for measuring tools I have a first generation Mitutoyo 6" digital caliper and a two year old version of the same. The both perform exactly the same with zero issues (except for me stupidly measuring a rare earth magnet once, miserable to demagnetize). Batteries last a year or more with daily use. I prefer these to my 35 year old Starret and Mitutoyo dials. Much less susceptible to debris/contamination. I don't view calipers as high precision instruments as they are only good to .001". HF calipers are good for woodworking.
I don't mind reading veneer micrometers but I recently acquired a very nice Mitutoyo digital 0-1" micrometer. Game changer for doing sub .001" work.