Data that self-destructs when the LN2 needed to keep it cool enough to "keep it stable" runs out? Sounds like a fun game of data Russian roulette.
The controllers will end up needing to be quantum computers just to handle the voltage states. Lol"But controllers capable of processing 128 voltage levels accurately might be as complex as microprocessors and just as expensive."
That is the very first thing that came to mind before reading everything in detail. I'm sure they'll find the right balance to do this at ambient temperatures or at least find an application where it works without "lab conditions", but the whole solution may not scale down to consumer pricing levels any time soon, if at all. Also, more voltage levels means more delicate voltage balance in the material, so I'm almost sure it will last way less than your normal MLC/TLC.
Cool to know they're trying hard to increase capacities though. That is like the last bastion HDDs hold really tight.