Meaning since the guy above had to paid to have his transaction entered,
PoW is not permissionless, if it requires payment to the miners. Therefore PoS is also not permissionless since transaction fees are also charged.
Ok, since you destroyed the useful meaning of the word "permissionless" for decentralized systems, let's call it
clonck. BTW, you can also object to the word decentralized, because no matter what, those systems will be centralized on earth, within the hands of (for the moment) members of the species Homo Sapiens. So let us replace "decentralized" by
blunck. As "trustless" is also impossible, because you had to trust your mother when she gives birth to you, let us call the new notion
flanck.
So we are trying to build systems that are
clonck, blunck, and flanck. Better now ?
We define
clonck as those systems for which there is no official authorisation to be demanded, and granted by a specific institution, in order to be able to try to participate in them with a non-zero chance of success. That is, a random external entity has a reasonable probability to succeed in participating in the system without any specially granted permission by any institution.
We define
blunck as those systems where at least 3, but preferentially very many non-colluding entities participate in such a way that they cannot, individually, determine most of what happens in the system.
We define
flanck as those systems that still have a reasonable chance to function correctly, even if an important fraction (to be determined) of the non-colluding entities (see the blunck property) are trying to cheat on the system or try to sabotage it and bring it down.
There.