My understanding has always been that the hardened centres were for tailstock use, as in normal use they are a lubricated bearing surface, and will wear (as the OP found out). The unhardened ones designed for the head end, as they are effectively locating only and not a running bearing surface – also that way so you could routinely re-shape that one with normal tools to ensure it was preciseley on centre.
So, if you’ve got a bit of an assortment of centres from different sources and mixed MT sizes, you may simply be using the ‘wrong’ type in one end or the other. Can’t think why you would have an unhardened half-center though, unless ,as suggested, it was just ‘faulty’
Mike