I see this as very hard to implement. There are several cases that can not be solved.
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One way sync could be achieved. But two way isn't possible. The reason is that we can not know if a geocache has been added to one of the sides, or removed from the other.
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The next issue is that we can not do this in real-time. It would then have to be daily syncs or similar. Which in my opinion would ruin the use case, and make it too unreliable.
However, I like the idea, if it would be achievable with the API from Groundspeak.