This is not a situation I've run into myself, so I also did a bit of digging.
As expected, it does not look like you can delete a Facebook page via their API -that's a lot of risk/liability for them and they typically like things like this done directly on the platform so they know the person completing the action has full admin rights and access. I can't think of a good reason this would be an option, especially one that would benefit Facebook as a platform.
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