Earlier quoted context omitted.
They are appointed by the elected(the governments of the countries and the European Parliament, which are all elected). When you say it like "they are not elected but appointed", you make it sound like some 3rd party is appointing them and you have no power on it but those who appoint the members of EC are the members of EP(elected every 5 years) and the national governments(elected accordingly to the local laws). If…
So they are not elected? Right? Therefore they are not accountable to the public.
Many important EU figures have been elected repeatedly for national parliaments, as national ministers or for leadership positions in major national political parties, and only after that got an EU job.
I think it's by design: The jobs are put together as a nationally/politically balanced team, picked from from a large set of candidates who have generally been accepted by national voters over a period of time.