Well, your assuming that just because it's near the same place as Illum, that it is Illum. For all we know, it's a moon or another planet in the system, or perhaps it is Illum's sun which was drained to power Starkiller Base.
I think it'd be interesting to make Starkiller Base another planet in the same system as Ilium, possibly the one slightly closer to the system's star.
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