My Starrett set, purchased in the late 50's, doesn't suffer from what you describe, although the one from .300/.400 bore size does have a slight radius, but nothing more than a few thou, so it is capable of measuring very shallow bores. The other three appear to have nothing more than a couple thou radius.
Mine are slightly less than a half ball, so the only limiting factor is the slight radius, a necessary evil to avoid cutting the bore while taking a reading..
Harold