Has anyone  bothered to measure just how much material is removed by the etching process?

Obviously, the strength of acid, kind of acid, the time spent etching, and the desired severity of etch all have an effect, but if a smith wanted a very dramatic topographic etch, are we talking a thousandth of an inch?  One ten-thousandth?

It's not hard to measure the depth of an etch.  Make a blunted pointed tip to fit over the end of a micrometer spindle and measure it.  Measure an etched verses unetched area and subtract and you will know how deep the etch is.

You will also have to consider the layer count. A thirty layer billet will be as said above....a one thousand will be another item entirely. You could also measure the billet, then remove the top layer and remeasure the remaining steel .