I'm always a bit puzzled by this objection - it seems a bit artificial to me. Unless you live in Maidenhead or you're a Tory MP, you can't get rid of Theresa May either, and wherever you live in the UK you have no say who the PM chooses as their cabinet. Democracy is always finite, and there has to be some element of appointment.
And if the EU's higher echelons were decided by one-person-one-vote across the EU, the President of the EU would almost certainly be German in perpetuity, since Germany is the most populous country in the EU - is that actually what you want? If your objection is genuinely about the way the EU is elected, but you can't suggest a better solution, then I suggest it cannot be a genuine reason and is just a reflection or a justification of your antipathy.
Personally (as a minority-party voter whose vote is almost always thrown away, or else has to be deployed tactically against the mainstream candidate I like least) I find it hard to accept that Westminster is any more democratic than the European Parliament (which is determined by PR, so the one place where I can vote with my conscience and still usually be represented).