I think you must have misread what I wrote because I specifically mentioned incentive.
> There is such a mining incentive in proof-of-stake, block signers get rewarded.
Not in all PoS coins, actually. And arguably you don't need it. Your stake's value is contingent on fulfilling the implicit promise of the network: honest, accurate, fast transactions.
There is such a mining incentive in proof-of-stake, block signers get rewarded.