BTC miners make around 20mil / day and with a 400B market cap, that's around 1.78% / year so definitely higher. But I'd argue the United States Mint also relies at least partly on the US military.
The Protection Department would not last long against a nation-state attack. In contrast, BTC has no nation-state or military protection.
It doesn't matter about the US military, because the gold market doesn't have to prop up the US military - it gets that ride for free. The point isn't "who is cheaper" in some theoretical sense, it's that as a practical matter the nation of Bitcoinia is importing a large amount of electricity from the USD, RMB, EUR etc economies. This is equivalent in effect to what the gold market as a whole has to pay in storage/holding costs for physical gold. If physical gold holding costs were to rise substantially for some reason, that would significantly reduce the returns available from holding gold.
The Protection Department would not last long against a nation-state attack. In contrast, BTC has no nation-state or military protection.