Bitcoin's decentralized and permissionless nature is its biggest advantage but also its biggest weakness: it's too easy to create fake nodes.
By running a full node (fake or real) you don't gain any kind of advantage or disadvantage. So you can't call "being easy to create fake nodes" a weakness. It also has nothing to do with bitcoin being permissionless and decentralized.
But I believe that a permissioned and decentralized network is also possible. For a node to enter the network, a 51% approval of validators already approved in the network is required.
The real question that you forgot to answer first is "Why would we want to prevent 'fake' nodes from entering the network". They certainly aren't gaining any kind of advantage and they also not capable of harming the network in any way since they will be banned quickly if they act maliciously.
Humans are very good at identifying bots.
They are also very good at abusing their power to some day start banning those who they don't like hence ruining the whole decentralized system.