In PoW, there is an unbounded cost to preventing anyone else from winning a block announcement forever. In PoS, there is a bounded cost. The shape of the curve that monsterer mentions never levels off asymptotically.
And that is why PoS can't be asymptotically permissionless, but in theory PoW can be.
That's actually quite an elegant description. It says that if I own all the stake in a POS coin, I control it forever, no one else can mine a block for the rest of its existence. In POW you can't own all the hashes in the world forever (unless you have infinite electricity) because every hash has a cost, so your monopoly is only temporary.
People will argue that owning all the stake in the world is unrealistic, but in actual fact your level of control is directly proportional to your stake, so you can start causing problems much sooner and potentially cost free if you are shorting the coin.
Your degree of control is superlinear in the amount of your stake.
TPTB, satoshi's system is permissionless period, for two reasons, one being that control of <50% (or maybe some lower threshold with later analysis) is an axiom. The second being that permission isn't necessary to break someone's 50% monopoly (unless the monopoly controls 50% of the energy in the universe or something), similar to the above argument.
This may seem useless in the real world, but that's a different question from the mathematical properties of the system itself. We start with a clear description of the mathematical properties and then apply to the real world. In the process of doing the latter various additional assumptions are inevitably made.