In the case of Vanuatu, I think it's to do with the country preserving its own individual unique resources - the stem pieces would have to be smuggled out and it is hard to do this with more than a handful. There is legislation on it, same as taking out any artefacts over a couple of decades old.
It's only a matter of time before someone comes up with a scheme though. You could fit a whole load of cuttings in a yacht.
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The Friends of Tikopia yacht group took Vanuatu cuttings to Tikopia, at the extreme eastern end of Solomon Islands a few years ago. It was during a humanitarian mission to rebuild their freshwater lagoon, where a cyclone had washed out part of the beach.
I'm not sure what the logistics would have been. Yachts can finalise departure paperwork in Sola, Banks Islands, and they'll give you a few days after clearing to keep poking around in Vanuatu. If there were a way to pre-clear the entry to Solo, the trip to Tikopia is only a day. However I don't even think there's a port of entry anywhere in Santa Cruz province. It may have been approved ahead of time due to the nature of the voyage, and any plant products that happened to be onboard were just happy accidents.
So it wasn't really smuggling. Tikopia was happy to receive the cuttings, and it is their island after all. It's not like a bunch of Aussies dropped anchor off Honiara with tonnes of illicit cuttings, Tikopia is a tiny poly outlier settled by Tongans, way out at the eastern extreme of Solomon Islands.