PoS blorkchains do not solve the first problem completely (they still require an obscene amount of power to do something that can be done way more efficient) but implement an entirely new kind of problem: The more tokens someone already had, the higher his chances in the "stake-lottery".
Essentially, PoS makes sure that "he who has the gold makes the rules" becomes hardwired in the system, instead of only being a side effect of it.
How "green" something is, is determined by how much resources one unit of what it does uses, compared to how much resources doing the same unit of work on an alternative system uses.
eg. a petroleum lantern produces light more efficiently than a campfire. However, neither of them is "pretty green" compared to a LED.
Compare the amount of energy per transaction required with a PoS system to the amount of energy required to do it with, say, a credit card.
PoS is just a bunch of computers largely idling. Whether it's 1k or 10k, it doesn't matter - there is no energy use to speak of, at least none that society has a legitimately interest in regulating.
The Tezos Foundation, who's interest is in advertising how green they are, claims in a year they consume as much electricity as 17 individuals (https://tezos.com/carbon/).
It is up to critics to provide evidence of PoS energy use being a concern; no one has done so, because the outcome is essentially is predetermined.
> It is up to critics to provide evidence of PoS energy use being a concern
So, is there evidence, as in peer-reviewed studies, that PoS blockchains can handle the volume of transactions of traditional financial systems while requiring LESS energy?
I don't know, but I don't see how that is an interesting question. As crypto critics rightly point out, the vast amounts of energy that the financial system consumes provides a huge amount of different services; from bank branches to regularity compliance.
From a literal technical point of view, storing a ledger on 10k computers consumes more energy than than storing it one one. But maybe the backup and operational infrastructure of a bank to manage that one centralized ledger consumes more energy than 10k PoS nodes. But then people also build all kinds of services around those blockchains which require their own computers. In both cases, you get something unique: the blockchain gives you permissionless financial network, your bank gives you a regulated one.
Meanwhile, a single branch of McDonalds consumes many multiples more energy than any PoS blockchain.
My point is really just this: Critics can try to critique PoS blockchains as useless. They may also try to ban them using arguments around say, securities laws or AML. But the energy argument is DoA.
