Should they eat their own dog food? Probably. But pretending there's some kind of hypocrisy going on is stretching it.
Let me assure you: there is absolutely no shortage of hypocrisy. You don't need anything more than to walk around their offices and ask what all those weird marking on public and private spaces mean. You'll be disgusted, and cured of any notion that the EU intends to do anything for anyone but themselves.
But outside of that, there are clear personal status cult being upheld everywhere around the European organisations, with the biggest distinction between the "fonctionnaires" and everybody else (although as an employee of the commission you're still several rungs above "les gens de la rue" (which does not mean homeless, like in France, it just means normal people of Brussels). And may God help you if you're working for ISS or any of the cleaning companies. At that point your status is so low that people routinely throw things at you just to cool their frustration. This is accepted and normal behavior, despite how incredibly immoral it is.
(The "European quarter" of Brussels has a ton of public and private spaces, from "public" parks to a small shopping center (with mostly cafes), and the highly coveted parkings and parking spaces that are reserved, by law, for European officials' use only. So does Woluwe, even if they're a lot better hidden there. To say that these people have no intention to use their power to improve people's lives is absurd when you walk around their offices)
The EU isn't a state it's a union of states and there is EU elections happening.
By that standard the Soviet Union, China and Saudi Arabia are/were democratic too. They all have/had elections. Elections that do not determine who has legislative and executive power are not elections.
The reason why is of course simple. People in member states do not care about the EU. They care about local politics 99% of the time. On top of that member states electorates do not agree on the issues. Not on what the issues are in the first place and certainly not on what is to be done about them. There is no way for politicians to campaign across the EU, it's all done locally. Therefore the assessment of most fonctionnaires in Brussels is probably correct: there is no way to have an effective democratic EU. They also asses that they don't want to do that, as it would not be a unifying force.
[1] https://en.wikipedia.org/wiki/Elections_in_the_Soviet_Union