Interestingly enough, its not a problem with PoS! PoS certainly has other problems (e.g., many fail to have effective consensus) but the monopolized entrenchment of leadership isn't fundamental. This issue applies to elected positions.

Consider the scenario in of PoS whereby all participants are actively staking. The inflation is thus being distributed proportionately to everyone -- and the effective inflation is zero. No one gains or loses over each other. When a PoS participant doesn't stake, they are forgoing their sort-of "right to protection against inflation", and this value is transferred to those that are staking.

You are certainly correct though that this is a pain point that PoW doesn't have -- because consensus is not determined from within the system, it is determined from outside the system.