You have to differentiate between consensus rules and how the blockchain is secured. Verifying if the consensus rules hold is equally simple in both POS and PO

You have to differentiate between consensus rules and how the blockchain is secured. Verifying if the consensus rules hold is equally simple in both POS and POW. But with Bitcoin's POW, the hashrate is part of the consensus rules by requiring the hash of the output block having a certain property which can only be attained in a timely manner with enough processing power and luck (in that sense, also in POW a block proposer is chosen "randomly"). With POS, you don't have the hashrate. But you have the stake which (in Ethereum's POS) is lost if you try to vote for more than one possible new block for the chain. Which is a direct economic incentive to behave correctly.