Add to that - I do not see any mention of the source of timing or "timestamp server" as the Nakamoto paper refers to it. The details of why it is important are in my blog post here https://grisha.org/blog/2018/01/23/explaining-proof-of-work/ (which was once at the top of HN).
I don't think your post shows that any public ledge must provide a timestamp server (which I think is your claim?). For instance PBFT (with a fixed validator set) works perfectly fine without providing a timestamp server since it's asynchronously safe - you can take as long as you want to complete every PBFT round.
Basically, PoW provides consensus by providing an absolute timestamp (we know that at the difficulty adjustment equilibrium, a certain block header must have taken 10 minutes to produce), but this does not imply that a consensus algorithm that all public ledger consensus algorithms must produce an absolute timestamp (the later claim is stronger).
My post merely shows that PoW is the mechanism via which this absolute timestamp (I like this terminology, BTW) is provided and seems very important, but I think the real question (to which I do not know the answer) is: can it be proven that an absolute timestamp is essential or non-essential, because it would answer the question of whether a distributed ledger without PoW (timelock puzzle) is fundamentally possible.
Yeah, I'll have to think a lot harder about full PoS to maybe answer that question. One thing to note us that there are certain hidden timing assumptions (eg in casper-ffg, there is the 4 month unbonding period, and the timescale over which an inactivity leak occurs) that are necessary for security (they seem to correspond to the time scales needed for weak subjectivity social consensus and hard forks respectively)
I think the most precise name might be something like "affine timestamp"; you don't actually need timestamp wrt the big bang but being able to measure the rate-of-time is stronger than merely being able to order events
Basically, PoW provides consensus by providing an absolute timestamp (we know that at the difficulty adjustment equilibrium, a certain block header must have taken 10 minutes to produce), but this does not imply that a consensus algorithm that all public ledger consensus algorithms must produce an absolute timestamp (the later claim is stronger).