Presumably it's considered useful because there's a measurable error rate in the nurse a) reading -and/or- b) recording the observed data. Assuming this thing works properly more often, you've not only guaranteed you get the data entered properly, but it's more likely to be right.
I imagine this is compounded by the subject matter being measured. A simple "click and lock the measurement" button would be invaluable when trying to measure the height of a squirming child.
Simple, easy to read numbers that eliminate guesswork would seem to make a nurse's job much simpler (or allow them to utilize people who are not registered nurses to collect this data). There have been similar advances in scales, blood pressure cuffs, heart rate monitors, etc. All are readable using analog gauges, yet they progressed to digital devices.
What people here don't seem to realize is that a doctors' scale or measuring tapes are not used for precision measurements anyway.
If the doctor sees the patient only every few months, individual variations (kids will grow, adults will gain (or, sometimes, hopefully) loose weight)) in body height or weight will exceed the precision you can get even out of the cheapest scale or measurement tape.
And as for the purpose of the measurements: The doctor will use the values acquired from the tools to categorize patients in categories: E.g. a obese person has a higher risk of cardiac arrest, someone looking quite anorexic will have other problems with his blood chemistry... And here a few kilograms/centimeters don't influence the general statement at all.
