An important distinction:
Impeachment does not overturn an election, it removes a President from office. The other half of the ticket, also duly elected, becomes President. The loser of the previous election remains a loser.
Impeachment is not a question of “overturning the voice of the people”, it is a question of whether a servant of the people, trusted and selected by the people, has violated the oath of office and, therefore, the trust of the people.
Being elected by the voice of the people to the highest office in the land shouldn’t absolve someone from the expectations of lawful and ethical behavior, it should punctuate their importance.