Surely, camera height would be decided by the composition, not by optical geometry? Would not the priority be to place the lens where aesthetics demanded and apply movements afterwards as required?
It’s true that if something is very close in the foreground, then more extreme movement may be needed. Moving the camera away, which could be either either upwards or backwards, will alleviate this. This confirms your supposition.
Much will depend on what else is in the frame. If you are photographing a flat plane, a picture of a bowling green, perhaps, you should be able to get good focus from any height. Clearly the perspective would change as the height changed. If there’s a person in the picture, that would complicate matters. The tilt used for the grassy surface would give them sharp shoes and a fuzzy head. You might be making a comment on bowls players of course, but that’s another matter.
For a very complete discussion of camera movements, see Harold Merklinger, available as a free PDF download. He explains much more than I ever wanted to know.