Look, Bitcoin does NOT have to be all or nothing. That's, I think, what people here are most confused about. They think if there is one small way bitcoin can't perform like dollars or gold then it is totally useless.
That is not the case. Bitcoin doesn't have to replace fiat currencies; it doesn't have to replace using precious metals. It can be used alongside anything as people wish, and have value where ever it does. Remember Liberty Dollar and eGold? Did those currencies fail while they were in use because you couldn't use them in a remote village? You couldn't use eGold without power either, but it was very successful and had value until the feds shut it down.
Anyway, to answer your direct question about power there are ways to use bitcoins without power. Two ways being experimented with are physical bitcoins and paper notes.
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