I think a better example would be high speed trading and similar. Of course any big corporation or administration is going to have a lot of underused ressource

I think a better example would be high speed trading and similar. Of course any big corporation or administration is going to have a lot of underused ressources and redundancy but it doesn't mean they burn power "for the sake of it" as bitcoin does. Also, bitcoin is not a bank, it's supposed to be a currency. If big banks were to switch to bitcoin I don't think they would spend less energy doing all you said. So no matter what you think of bitcoin it's fair to say it's not very "green" so far.