I used an industrial/pilot sized freeze dryer at a research facility in Auckland. I had some green kava juice left from my experiments with bottling kava and decided to freeze dry some just for fun/research. Took me a couple of attempts and playing around with the settings, plus using some additional tools, but I think the end result was fairly close to the taste/smell/texture of the actual green juice. In that case the juice itself was quite oxydised and made from less than perfectly prepared kava, so the end result wasn't spectacular, but still not much was lost in the process. One advantage of freeze drying over standard dehydration is that it makes the powder a lot easier to rehydrate (literally a quick stir and everthing is rehydrated with no clumps).
Freeze dryers are quite power hungry and the whole process is quite labour intensive. Another problem with freeze drying is that it can't possibly kill or even reduce any mirobial content, so you either have to start with pristine roots or need to take a couple of extra steps to ensure you end up with a clean product.
I'd say it's all fairly easy to do, but ultimately makes little commercial sense outside of the kava growing regions. Making instant kava (with or without a freeze drier) makes far more sense when youv'e got access to freshly harvested roots than when you have to send them across oceans. It takes around 10-12kgs of fresh green roots to get 1kg of instant if I remember correctly. In general, all kava processing should best be done as close to the kava gardens as possible*. And it is already done. Our supplier of green instant (instant made from green, but without a freeze drier) processes it all into powder within literally hours of receivign freshly harvested roots. The end result is fantastic. I guess they could maybe try using a freeze drier if there was a lot of demand for it, but I am not sure many people would be keen to pay, say, 10-20% more for instant kava for it to taste a bit more like green. Especially when it's hard to avoid oxydising the juice when you prepare it for freeze drying.
*The only possible exception is bottling kava made from dry powder, as this effectively involved adding a lot of water (and weight) to the product and it's likely much cheaper to do so closer to customers than closer to the gardens.