And because so-called Improved Buildings have just tiny changes, it seems much easier to justify having a second Improved Building of the same type than doubling up on a different category. A Stone mine or a gold-tricking Garden, for instance, would feel really derivative, particularly with so many open areas in other Buildings available.
Not necessarily. In a vacuum sure, but for a civ that a stone mine meshes well with, it could be very welcome. Not to mention if we continue to look at the vacuum then Stone Mines are merely a part of the total civ. The total civ has other features, possibly age up methods/prereqs and a unique military lineup that might overshadow the fact that yes, they have a stone version of the gold mine to the point that you would never mistake the civ for Celts. It isn't lazy design if it actually fits the civ very well.