Speaking only for myself, I found the mapping of Kimle-Károlyháza quite surprising. It wasn’t where I thought the previous discussion was leading. We now have two objects that repeat almost the same tags including railway=station and public_transport=station. How would mappers know which one belongs in a stop area relation, for example? Note there is also an ongoing discussion on this forum about removing duplicate railway=station which informs mappers that there should be strictly one of these objects per station: Maproulette challenge: Fix duplicate railway stations [looking for feedback]
Also, I feel it is unclear whether you are asking for rendering specific to train stations or more generally. Is there any reason to treat stations differently from hospitals, shopping centres, or universities?
Given the low usage of type=label and the fact that the only documentation seems to be a proposal from 2008 that went no further, I would say it is going to be difficult to get this type of relation rendered.
I think it is rather different from the administrative boundary situation, where it is not quite true to say that the Chicago label is only rendered once - the label also appears alongside the boundary line if you zoom in far enough.