This is hypothetical - the glasses don’t fact-check what people say, they somehow detect willful deception, like people expect polygraphs to do, but with high accuracy. Would people welcome these, fear them, object on privacy grounds? I think it would be very contentious. Would people feel different if they only fed the information to the wearer but didn’t record or send it anywhere? What exactly would the issues be?
Probably not - for example, out of the half million or so elected officials in the US, only a couple thousand are full-time politicians with no other job. And even if all of them got kicked out of office the jobs would still exist and would go to other people.