Mining bitcoins is useless work to exactly the same extent that mining gold is useless work. > which means that the electricity used up by the Bitcoin network

Mining bitcoins is useless work to exactly the same extent that mining gold is useless work. > which means that the electricity used up by the Bitcoin network would be much larger on any reasonable measure than what you need to maintain other currencies This is only true if the other currencies are fiat money. For a non-fiat currency, it is necessary that either (i) it is hard to make (or people will just make enormous amounts and its value will go away), or (ii) it has intrinsic value.