How old coins can be more valuable? It has same value like Bitcoins that were mined yesterday.
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You are theoretically right if you only look at the price, although in the past there were stories about some miners selling newly mined coins at a premium price. Also, some could use such coins for tax avoidance purposes - because for example, I don't have to pay tax on all crypto investments made before January 1, 2016. Of course, you need to prove something like that, and the first step is to have coins that have been sitting at an address for a very long time.
What could go wrong here?
It makes sense to avoid taxes in this way, but there are probably other ways, at the same time with a much lower risk, while not sharing private keys with anyone.