It is a limitation of democracy. It is a limitation of every possible system of decision making. That, by definition, is it not working fine.

But it is not the limitation of democracy. Whatever people end up vote for is not the concern of democracy. By definition democracy is merely a system where people exercise power by voting, it doesn't concern about the outcome.

As long as people have the right to vote, it is a democracy.

Its not the concern of democracy if the people vote for the "wrong" politician.

People don’t exercise power in this scenario.

if they vote then they did exercise power (even if they vote for lying politician).

If they are not allowed to vote then they didn't exercise power.

There is no power to be exercised in this scenario. They can vote, but it is literally mere coincidence if anything related to their intentions occurs. It’s like typing onto a keyboard that isn’t plugged in. Or prayers to a non-existent deity. Voting ceases having anything to do with reality the moment reality stops having anything to do with the decision behind the vote. It is action without a discernible causal connection to the result.

(Is it just me, or does our disagreement sound like two people arguing if a tree falling alone in a forest makes a noise, because one thinks “noise” is the vibration and the other thinks it is the qualia?)

The power to be exercise is the casting of the vote.

The decision or the intention behind the vote is nothing to do with democracy itself.

Someone who cast a random vote in the ballot is as valid as someone who put a lot of thought in the ballot.

Doesn't matter if let say majority of the people vote by throwing the dice, it still democracy.