Focusing by changing tube length is not ideal at higher NA. Once you go over NA 0.6 or so, very few milometers count.
I don't understand the very few millimeters part.
Also you probably cannot do focus stacking easily, when your magnification changes during focus.
A very tiny change might be noticeable since the rays may not be perfectly parallel, so if that tiny change is the magnification changes mentioned, then yes that would require some calibrated scaling of the image to image stack. I'm trying to figure out if that is a real issue or not. Thor Labs sells a cerna set up with a z-motored objective holder below a static mounted epi. I asked them about it. The only other usage maybe is automating parafocal changes. But buy Thor I would assume would mean spending the money for matching objectives.