PoS put to rest:
PoS coins use the number of coins held as the basis for their signalling system. Since coins have an exchange rate, they obviously do not fulfill the criteria of having no value, either practical or intellectual. Thus PoS is not an viable mechanism for honest signalling.
Latter emphasis mine.
Could you provide a practical example where this would actually matter?
Intra- and inter-cellular biological systems like humans, signalling is effectively PoW. When this is circumvented, you get cancer or other cellular malfunctions. We aren't really special. The behavior of a cell is an abstraction of its composite parts. Likewise, we humans are an abstraction of our composition. We interact with each other, and without reliable means of signalling, bad things happen. A global PoW-based signalling network, as set out by S. Nakamoto, is the final primary invention necessary to achieve a Tier 1 society.
Non-PoW signalling mechanisms have uses, but there is always a tradeoff, and they cannot replace PoW. With imperfect signalling, you get the corrupted outsomes of socialist systems, and the corrupted outcomes of capitalist systems. Both work on paper, and the failures of each result from the same cause: failures in signalling. Imperfect information, asymmetric information, or good information but too slowly (which is a form of asymmetry).
As information asymmetry trends to zero, and the propagation time of perfect information trends to zero, the difference between the endgame of a socialist and a capitalist system trends to zero, and we achieve a tier 1 society.
Given two alternative theories of how things might become, theories of identical predictive ability, the simpler one is best, and more often right. This is Solomonoff's Law of Inference. The complement of this is for the same reason, from the same math, and dictates that the more computationally-complex description of the vector toward the past, given merely that it exists alongside a simpler one, is harder to forge by accident or maliciously, and therefore can be assumed true with a given probability weight. These things are all intertwined with the very nature of entropy and causality and the universe itself, and cannot be circumvented, no matter how warm and fuzzy a "greener" (or more frightful still, "fairer") proof system makes one feel. In fact, any time a non-PoW system is used as if it were a PoW system, it will be less "green" in the long run, although it may deceive cells or people in the short run if they are not immune to the deception.