Yes, and nobody needs that. One only needs ORDER, not "real world time proxies".
And how do you think you arrive at the order? Without reliable time-stamping, you don't and cant. It is the building block upon which all this is based.
In proof of work, if you do slightly more work than the "good guys" (that is, the ensemble of miners that were working "honestly"), you won. It is sufficient that you have proven, say, 50% more hashes than the "good guys" your chain will take over. With a digital signature, that is not "50% more", but 2^128 times more or so.
'Slightly more' work than the rest of the network is vastly more work than solving a single block.
They are only vulnerable to attacks from the inside, that is, from their owners, and then it depends exactly on the PoS scheme used. They cannot be attacked from the outside, from someone who doesn't have any stake in the system and never owned some stash. As to the exact attacks that are possible, that depends on the precise implementation of the PoS scheme.
If I pay 100% of staking, stake-owners to send a transaction to themselves at at precisely 12:00pm next monday, whichever chain I choose would be stalled forever. That's a fairly obvious external 'attack'.
PoW can even be attacked with all users offline, because the PoW stake holders have nothing to do with the coin. If tomorrow, the Chinese government confiscates most of the mining equipment, bitcoin is in the hands of the Chinese government. With a PoS coin, that's simply impossible.
Sorry, that's just plainly incorrect. If the chinese government confiscates all mining equipment in china, bitcoin blocks will slow down as the rest of the world gradually takes up the slack. On the other hand, if some force confiscates all the staking stake from a PoS chain, the chain is dead forever barring a hard fork.