I have been following Dr. Kevin Novak's youtube channel for a while now. And although he does a few things that I find unnecessary, like rip up a perfectly good carpet of montecarlo and Dwarf baby tears because there is detritus buildup below it, a lot of what he speaks about is rooted in sound science, eg a plenum for any planted tank, fertilising during photo-period etc.
For a planted tank, according to me the only disadvantage of anoxic filtration would be space. As a biocenosis bucket with a sump would take more space than a standard canister filter, especially since you have to increase the no.of buckets according to your livestock load. From his videos you can see that his backend is almost as large, if not larger than his front end.
The basic fact is that plants prefer ammonia to nitrates, so in theory, if his anoxic filter is working 100%, all his plant growth is solely due to ammonia as a source of nitrogen. From his recent videos, you can also say that his tanks are overstocked, but the argument he presents is that since his plant mass is keeping up with the ammonia supply along with the anoxic filter doing its job, there should be no detectable ammonia left in the tank. The anoxic filter converts through multiple processes, ammonia to gaseous nitrogen which is released to atmosphere. Not sure if the laterite plays a part in provinding a constant source of iron supply to the plants too.
TLDR: Anoxic filtration too large of a setup for most people. Yes it works. No plants wont starve.