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If all miners and all nodes quite bitcoin today, a person could buy themselves an ASIC or two (hopefully at a steep discount due to the recent events) and begin to mine blocks. They could move spend their bitcoin when they mine a block. (Although spending at this time would equal sending to another address that they control or burning the coins).
I'm sure there's some philosophical exercises to be had here, but I'm not too interested in them.
Bitcoin is a permissionless system. Therefore it cannot rely on other people doing anything. When Satoshi mined the first few blocks, he was using bitcoin and possessing it, even though no one else was on the network.
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At first, I thought the question is just navel gazing, but it might be more important than I immediately perceived.
Because your conclusion, "Any system that can be affected by questions of ownership as opposed to possession is not Bitcoin", seems to presuppose a strong philosophical concepts of possession as well.
For example, if one day miners and nodes stop relaying or mining certain transactions, can't you say that the holder of the private key still "possesses" the UTXO, they can just no longer spend it? Your concept of possession seems to import a notion of useability that puts requirements upon people other than the possessor (you impose requirements on the miners and the nodes).