The comparison to roles such as the current Secretary of State for Defense of the US is quite an important one. None of the last four holders of that office was ever elected at all, and even those who had held an elected position had long since vacated it, going back to at least 2000. Nor is this unusual for US high offices.
On the other hand, that isn't very democratic either -- and perhaps even more surprisingly so when the US tends to elect as many officials as possible, even going as far as electing judges. Presumably the point is that, at the federal level, the person held accountable for all federal decisions is the President themselves. But it still is more or less the same set-up as the EU -- where, despite the lack of electability of EU Commissioners, at least the other three major institutions of the EU (Parliament, EU Council, and Council of the EU), are made up of elected members, be they the elected Heads of State or elected Ministers, or elected MEPs.