51% coalitions can also create alternate histories in PoW by agreeing to run a modified version of the client. There is negligible thermodynamic cost to rewriting history when you control a majority of the nodes.
Pow is really an incentive system to keep selfish miners flocking to one chain, by making betting on one chain more profitable than betting on lots of chains at the same time.
The PoS challenge is to do the same without the egregious amounts of wasted energy, by making miners bet their money directly, instead of indirectly through their computers and electricity.
Running a majority of the nodes does not give you the ability to arbitrarily decide to accept an alternate history. One of the big value adds of bitcoin is that every node can decide on its own, without consulting other nodes, whether a transaction is valid or not.
There is absolutely a thermodynamic cost to reversing a transaction in bitcoin. Having the miners run an alternate client doesn't change that.
Pow is really an incentive system to keep selfish miners flocking to one chain, by making betting on one chain more profitable than betting on lots of chains at the same time.
The PoS challenge is to do the same without the egregious amounts of wasted energy, by making miners bet their money directly, instead of indirectly through their computers and electricity.