How is that antidemocratic?

Subsidiarity. National governments have a democratic mandate to govern their respective countries. They are not elected to govern Europe. We designate MEPs for this; they have little institutional power. The EU institutions are, by design, opaque and undemocratic in their functioning. I thought that this was generally acknowleged here, but I haven't been around much lately.

In the same vein, if a national government dismisses elected local governments and appoints prefects or governors to replace them, this is antidemocratic too, for the same reason : usurping legitimate democratic control.

This is definitely a mindset thing. If you don't conceive of the EU as a genuine entity with its own sovereignty, then an arrangement where it is governed by a syndicate of stakeholders (excluding the actual citizens) may seem appropriate. I'm frankly a bit puzzled that this mindset has such currency here.

_{It is rightly acknowledged that people of faith have no monopoly of virtue - Queen Elizabeth II}