With PoW, a miner needs to make an investment in mining equipment for to mine the cryptocurrency. If that equipment cannot be used to mine that cryptocurrency, there is no other way for the equipment to create value for its owner. If the miners as a whole were to act badly, the mining algorithm could be changed, and the mining equipment would become worthless.
Similarly, with PoS, a miner must "lock up" their coin in order to receive mining rewards. This is similar to a miner buying a miner, except without the mining manufacturer. If a PoS "miner" were to produce invalid blocks, their "locked up" stake would be lost. It would be up to the other PoS "miners" to determine if another miner is producing invalid blocks. If the miners as a whole were to act badly, the value of the coin would become worthless.
In both PoS and PoW, if the miners as a whole act badly, they will lose their investment. However, with PoW, the underlying coin will survive. This is an important distinction. If a large PoS miner were to successfully act badly, they could potentially enter into derraritive contracts to offset the coin they have "locked up" that is mining. This removes the requirement for a PoS miner to actually invest in their "mining" operation. OTOH, a PoW miner cannot easily hedge their investment if they intend to act badly while mining.
Maybe some algorithm that doesn't utilize cryptographic algorithms (I.e. energy) or tokens is what is necessary to create a low-energy PoW alternative that doesn't put your coins at financial risk (locking tokens I.e. POS).
For example - Proof of Time (I made this one up).
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If you remove the requirement that a miner/node needs to "work" in order to find a block, it will become trivial for a single entity to create an ~unlimited number of "miners" from a small number of computers.
Regarding your specific proposal, network connections among all nodes are not going to have a small enough latency for it to work. Also, it is not uncommon for different nodes to have a slightly different times for a variety of reasons. Bitcoin's implementation of PoW, for example, allows for nodes to have their time be by up to 2 hours.
Your proposal also made me think of another reason why PoS is inferior. With PoS, if you are connected to a set of nodes, you have no real way of knowing if you are receiving a valid copy of the blockchain. More specifically, if you receive two copies of the blockchain, you do not have a good way to validate which copy is correct. With PoW, if a node is sent two copies of the blockchain, it is trivial for the node to determine which version is valid because it can trivially calculate which blockchain has the greater amount of total work.