In addition to what has already been said, universal voting does not sound normal to my ears. We normally say: 'We do not have a say in voting her in or out'. Or 'she is not chosen by democratic vote.'

First sentence is fine. "They are, therefore, never eliminated by voting" isn't natural. Here's a few suggestions on rewriting it: 1: "They aren't answerable to the people, so why would they care about the people's voices?" 2: "They can't be voted out, so why would they care about the people's voices?" My preference would be #2.

Thank you!

I would prefer "Neither she nor the government are elected. They are, therefore not eliminated/removed by voting..."