Proof-of-stake replaces this massive electricity waste with game theory. Every validator must put up a deposit (in ETH) to participate. If it cheats, it loses that deposit. The damage it can do to the network is limited to less than the deposit. Therefore, it's never profitable to cheat - and so they won't, or if they do, they will go bankrupt, remove themselves from the network, and self-limit the problem. And transaction validation can now be split among thousands of nodes (instead of having those thousands of nodes all validate the same PoW), which means the network can scale to tens or hundreds of thousands of transactions per second.