Technically, Cait Sith is a cat robot controlled by Reeve, and Reeve wants to help the Planet. So even when ShinRa got "blown up", Reeve still had the desire to help out any way he could, and one of the methods he chose was to keep using Cait Sith. I'm not sure why we never see the oversized moogle that he was riding in all the other appearances of Cait Sith.
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