Arguably, the Iranian people have more stake in the matter than we in the West do, and just the process of going through a regime change will make a huge impact in Iran, particularly given the ongoing "Green Revolution" protests. All of those and other factors (like the power-grab struggle that's been going on over there the last few years) will affect the political situation over there in unknown ways, especially if Khamenei dies without any warning (which this seems to be).
That the world is eventually going to have to go on after Khamenei's death does not address the unpredictability problem I'm talking about if these rumors are true. Having an idea of his health and being capable of preparing contingencies happens to be part and parcel with diplomatic and foreign relations. That this would come up without any further notice seems both strange and, considering the lack of news in Iran on the matter, indicative of a political trick.