But it does. "Persona", etymologically, means 'mask' (Per = through, Sonare = Speak. As in, 'the thing you speak through', context: Plays and such, where you'd wear a mask). But I doubt you'd have any luck telling Merriam and Webster to update the definition of 'Persona' and mention only the mask thing.
Words mean what the majority thinks they mean.
Democracy as a word has been used as a word that means, mostly, that there are elections. The specific notion that the people decide directly is usually referred to us 'direct democracy'. A very wide ranging set of systems which all have in common that, primarily, some chunk of the populace gets to vote politicians out of office, has been called 'representative democracy'.
In the case of 'representative democracy', the 'democracy' bit still means 'power' for 'the people'. It's just that the 'power' that 'the people' have is specifically the ability to vote in (and out) a bunch of representatives who then decide.
Perhaps it is disappointing that this model didn't do what you wanted it to do here (which is: Presumably said representatives should decide to do what the people want them to do), but to lean on etymology to claim that this isn't 'democracy', that's just fallacious reasoning.