Does It Make Sense to Refer to EU Officials as Unelected Bureaucrats?

The Economist explains:

The EU, with about 33,000 civil servants, is dwarfed by the British government, which employs over 400,000. The complaint might be that not only junior EU officials, but many senior ones are appointed rather than elected; yet this, too, is true of all governments. British papers that disparage the “unelected” Michel Barnier, the EU’s lead Brexit negotiator, would struggle to find a country that has an elected trade representative.