It's just yet another level removed from the voters. If representative democracy is imperfect, then having another level to represent the representatives is more imperfect still.
I want the EU council to hand over many of its powers to the parliament and commission. (I’m fine with the parliament itself proposing and voting on the commission head, I’m not in favor of a directly elected head – but that’s just the German in me speaking where the federal government is set up exactly that way.)
It‘s the national governments standing in the way of that, not the EU itself.
The flip side to this argument is that it's harder to have a demagogue in the executive if they are indirectly elected. Or worse still a plutocrat dressed up as a demagogue.