It shouldn't be worthless but it should be worth less than bitcoin you control the keys to.
Right. To some degree all of us who hold our own keys believe this is true.
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I want to liken it to the fact that there always has been a premium to buy physical gold over paper gold. My intellectual bias says that makes sense because physical is better than a paper promise but it probably has to do more with the transport, storage, retailing costs that put a premium on it. But people buy it so I suppose they do value it more or they would buy the paper promises.
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