Sure, but can't the same apply on Proof-of-Work too? Say that the chain splits to old-Bitcoin and new-Bitcoin that supports merged-mining. Miners that mine the old chain can use redundant hashes to mine for the new chain, with the exact same hash rate. All that's needed for new-Bitcoin is to prove you've worked for it. It'll be essentially a sidechain, but with no dependence on the mainchain.
I don't see how Proof-of-Stake defeats the point of split. It's not the miners/stakers who define the value of the coins, but the users. If a split occurs, there might be new money created, but the product remains the same. Market value of 1 BTC is just split to 1-old-BTC and 1-new-BTC.
But the chains become independent once they split. The hashes would be different for different blocks, so you'd either have to choose to point your miners at the new or the old chain.I don't see how Proof-of-Stake defeats the point of split. It's not the miners/stakers who define the value of the coins, but the users. If a split occurs, there might be new money created, but the product remains the same. Market value of 1 BTC is just split to 1-old-BTC and 1-new-BTC.
The miners that believe they can make more out of the new chain would point their miners at the new chain, and miners who think they can make more out of the old chain would stay on the old chain.
The new chain would have different consensus parameters, which could not be subverted without significant cost to the miners who wish to subvert it.
Under PoS, this is not the case.
Since the staked amount persists on both tails, stakers could just stake the same way on both tails, and subvert the new chain, and its consensus parameters would end up being the same as the old chain.
That's exactly correct. That's one of the aspects that (asterisk asterisk except in niche constructions / exceptions) makes PoW so different and so much stronger than PoS. In PoS, the 'investment' (miner / stake) is within the system and that's a problem on a multitude of levels.The new chain would have different consensus parameters, which could not be subverted without significant cost to the miners who wish to subvert it.
Under PoS, this is not the case.
Since the staked amount persists on both tails, stakers could just stake the same way on both tails, and subvert the new chain, and its consensus parameters would end up being the same as the old chain.