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 No, it means a P2P.

Equality of opportunity, not equality of outcome. There is no centralized party deciding who can and can’t be a peer. 

Bitcoin is not perfect. It’s good enough and the best we have. 
 Right. The opportunity to hit the main chain doesn't exist without changes to scale UTXO ownership. This is irrespective of fees. Thank you for confirming for me.  
 Of course it exists, what are you talking about? Anyone that wants to transact on-chain can do so at any time.  

The network is and will continue to be P2P. Show me an example of a peer of the network not being allowed or requiring permission to transact with another peer. 

The elephant in the room is that not everyone will end up being a peer. Bitcoin is scarce, blocks pace is scarce. This is not a new revelation. 
 How do you define a peer of the network?
Do think everyone will have an equal opportunity to be a peer? 
 Anyone can run the software and participate in the free market for scarce UTXOs and blocks pace.

I’ll leave it there. We can agree to disagree on the outcomes we want and how to get there.